• Overall Survival (OS) [ Time Frame: Up to ~48 months ]
  OS is defined as the time from randomization to the date of death due to any cause.
• Progression-free Survival (PFS) Per Response Evaluation Criteria in Solid Tumors Version 1.1 (RECIST 1.1) [ Time Frame: Up to ~36 months ]
  PFS is defined as the time from randomization to the first documented progressive disease (PD) or death due to any cause, whichever occurs first. Per RECIST 1.1, PD is defined as ≥20% increase in the sum of diameters of target lesions. In addition to the relative increase of 20%, the sum must also demonstrate an absolute increase of ≥5 mm. Note: The appearance of one or more new lesions is also considered PD. PFS will be assessed by blinded independent central review (BICR) per RECIST 1.1, modified to follow a maximum of 10 target lesions and a maximum of 5 target lesions per organ.

• Objective Response Rate (ORR) Per Response Evaluation Criteria in Solid Tumors Version 1.1 (RECIST 1.1) - Pembrolizumab+Lenvatinib vs. Docetaxel [ Time Frame: Up to ~18 months ]
  ORR is defined as the percentage of participants who have a Complete Response (CR: Disappearance of all target lesions) or a Partial Response (PR: At least a 30% decrease in the sum of diameters of target lesions). ORR will be assessed by BICR per RECIST 1.1, modified to follow a maximum of 10 target lesions and a maximum of 5 target lesions per organ.
• Objective Response Rate (ORR) Per Response Evaluation Criteria in Solid Tumors Version 1.1 (RECIST 1.1) - Pembrolizumab+Lenvatinib vs. Lenvatinib Monotherapy [ Time Frame: Up to ~36 months ]
  ORR is defined as the percentage of participants who have a Complete Response (CR: Disappearance of all target lesions) or a Partial Response (PR: At least a 30% decrease in the sum of diameters of target lesions). ORR will be assessed by BICR per RECIST 1.1, modified to follow a maximum of 10 target lesions and a maximum of 5 target lesions per organ.
• Duration of Response (DOR) Per Response Evaluation Criteria in Solid Tumors Version 1.1 (RECIST 1.1) [ Time Frame: Up to ~48 months ]
  DOR is defined as the time from first documented evidence of Complete Response (CR: Disappearance of all target lesions) or a Partial Response (PR: At least a 30% decrease in the sum of diameters of target lesions) until disease progression or death due to any cause, whichever occurs first. DOR will be assessed by BICR per RECIST 1.1, modified to follow a maximum of 10 target lesions and a maximum of 5 target lesions per organ.
• Number of Participants Experiencing an Adverse Event (AE) [ Time Frame: Up to ~48 months ]
  An AE is any untoward medical occurrence in a clinical study participant that is temporally associated with the use of study treatment, whether or not considered related to the study treatment. The number of participants who experience an AE will be presented.
• Number of Participants Discontinuing Study Treatment Due to an AE [ Time Frame: Up to ~48 months ]
  The number of participants who discontinue study treatment due to an AE will be presented.
• Change from Baseline in European Organization for Research and Treatment (EORTC) Quality of Life Questionnaire-Core 30 (QLQ-C30) Combined Global Health Status / Quality of Life (Items 29 & 30) Scale Combined Score [ Time Frame: Baseline and Week 12 ]
  The EORTC QLQ-C30 is a 30-item questionnaire developed to assess the quality of life (QoL) of cancer patients, including a combined global health status (GHS)/QoL (Items 29 and 30) scale. For each item, scores range from 0-100, with higher scores indicating higher GHS/QoL. Per protocol, scores for items 29 and 30 will be averaged to compute a combined GHS/QoL scale score. Change from baseline in the combined GHS/QoL scale score will be presented.
• Change from Baseline in EORTC Quality of Life Questionnaire Lung Cancer Module 13 (QLQ-LC13) Cough (Item 31) Scale Score [ Time Frame: Baseline and Week 12 ]
  Used in combination with QLQ-C30, the EORTC QLQ-LC13 is a supplemental lung cancer-specific module, including a single-item scale score for cough (Item 31). For this item, individual responses to the question "How much did you cough?" are given on a 4-point scale (1=Not at all; 4=Very much). Scores are transformed to a range from 0-100, with a lower score indicating a better outcome. The change from baseline in the EORTC QLQ-LC13 cough (Item 31) scale score will be presented.
• Change from Baseline in EORTC QLQ-LC13 Chest Pain (Item 40) Scale Score [ Time Frame: Baseline and Week 12 ]
  Used in combination with QLQ-C30, the EORTC QLQ-LC13 is a supplemental lung cancer-specific module, including a single-item scale score for chest pain (Item 40). For this item, individual responses to the question "Have you had pain in your chest?" are given on a 4-point scale (1=Not at all; 4=Very much). Scores are transformed to a range from 0-100, with a lower score indicating a better outcome. The change from baseline in the EORTC QLQ-LC13 chest pain (Item 40) scale score will be presented.
• Change from Baseline in EORTC QLQ-C30 Dyspnea (Item 8) Scale Score [ Time Frame: Baseline and Week 12 ]
  The EORTC QLQ-C30 is a 30-item questionnaire developed to assess the QoL of cancer patients, including a single-item scale score for dyspnea (Item 8). For this item, individual responses to the question "Were you short of breath?" are given on a 4-point scale (1=Not at all; 4=Very much). Scores are transformed to a range from 0-100, with a lower score indicating a better outcome. The change from baseline in the EORTC QLQ-C30 dyspnea (Item 8) scale score will be presented.
• Change from Baseline in EORTC QLQ-C30 Physical Functioning (Items 1 to 5) Scale Combined Score [ Time Frame: Baseline and Week 12 ]
  The EORTC QLQ-C30 is a 30-item questionnaire developed to assess the QoL of cancer patients, including a physical functioning (PF) scale (Items 1 to 5). The PF scale consists of participant responses to 5 questions regarding performance of daily activities [1) strenuous activities; 2) long walks; 3) short walks; 4) bed/chair rest; and 5) needing help with eating, dressing, washing themselves or using the toilet]. Overall PF scores range from 0 to 100, with a lower score indicating a better outcome. The change from Baseline in the EORTC QLQ-C30 PF (Items 1 to 5) scale combined score will be presented.
• Time to True Deterioration (TTD) in EORTC QLQ-C30 Combined Global Health Status / Quality of Life (Items 29 & 30) Scale Combined Score [ Time Frame: Up to ~48 months ]
  The EORTC-QLQ-C30 is a 30-item questionnaire developed to assess the QoL of cancer patients, including a combined GHS/QoL (Items 29 and 30) scale. The TTD in the combined GHS/QoL (Items 29 & 30) scale combined score will be presented, defined as the time to first onset of a ≥10 point decrease from baseline.
• Time to True Deterioration (TTD) in EORTC QLQ-LC13 Cough (Item 31) Scale Score [ Time Frame: Up to ~48 months ]
  Used in combination with QLQ-C30, the EORTC QLQ-LC13 is a supplemental lung cancer-specific module, including a single-item scale score for cough (Item 31). The TTD in EORTC QLQ-LC13 cough (Item 31) scale score will be presented, defined as the time to first onset of a ≥10 point decrease from baseline.
• Time to True Deterioration (TTD) in EORTC QLQ-LC13 Chest Pain (Item 40) Scale Score [ Time Frame: Up to ~48 months ]
  Used in combination with QLQ-C30, the EORTC QLQ-LC13 is a supplemental lung cancer-specific module, including a single-item scale score for chest pain (Item 40). The TTD in EORTC QLQ-LC13 chest pain (Item 40) scale score will be presented, defined as the time to first onset of a ≥10 point decrease from baseline.
• Time to True Deterioration (TTD) in EORTC QLQ-C30 Dyspnea (Item 8) Scale Score [ Time Frame: Up to ~48 months ]
  The EORTC QLQ-C30 is a 30-item questionnaire developed to assess the QoL of cancer patients, including a single-item scale score for dyspnea (Item 8). The TTD in dyspnea (Item 8) scale score will be presented, defined as the time to first onset of a ≥10 point decrease from baseline.
• Time to True Deterioration (TTD) in EORTC QLQ-C30 Physical Functioning (Items 1 to 5) Scale Combined Score [ Time Frame: Up to ~48 months ]
  The EORTC QLQ-C30 is a 30-item questionnaire developed to assess the QoL of cancer patients, including a physical functioning (PF) scale (Items 1 to 5). The TTD in PF (Items 1 to 5) scale combined score will be presented, defined as the time to first onset of a ≥10 point decrease from baseline.

• Biological: Pembrolizumab
  IV infusion of pembrolizumab at 200 mg
  Other Names:

  • MK-3475
  • KEYTRUDA®
• Drug: Lenvatinib
  Oral capsules (unit strength: 4 and 10 mg) at 20 mg or 24 mg total daily dose.
  Other Names:

  • MK-7902
  • E7080
  • LENVIMA®
• Drug: Docetaxel
  IV infusion of docetaxel at 75 mg/m^2.
  Other Name: TAXOTERE®

• Experimental: Pembrolizumab+Lenvatinib
  Participants receive pembrolizumab at 200 mg, every 3 weeks (Q3W) via intravenous (IV) infusion on Day 1 of each 21-day cycle, in combination with lenvatinib at 20 mg, once daily (QD) via oral capsule. Pembrolizumab will be administered for up to 35 treatment cycles (~2 years). Lenvantinib will be administered until progressive disease or unacceptable toxicity.
  Interventions:

  • Biological: Pembrolizumab
  • Drug: Lenvatinib
• Active Comparator: Docetaxel
  Participants receive docetaxel at 75 mg/m^2, Q3W via IV infusion over 1-hour infusion on Day 1 of each 21-day cycle. Docetaxel will be administered until progressive disease or unacceptable toxicity.
  Intervention: Drug: Docetaxel
• Experimental: Lenvatinib Monotherapy
  Participants receive lenvatinib at 24 mg, QD via oral capsule. Lenvantinib will be administered until progressive disease or unacceptable toxicity.
  Intervention: Drug: Lenvatinib

Inclusion Criteria:

• Has a histologically or cytologically confirmed diagnosis of metastatic squamous or nonsquamous NSCLC (Stage IV: M1a, M1b, M1c).

• Has PD on treatment with one prior anti-PD-1/PD-L1 monoclonal antibody (mAb) administered either as monotherapy or in combination with other checkpoint inhibitors or other therapies.

  • Retreatment with the same anti-PD-L1/PD-L1 mAb is acceptable in the overall course of treatment
• Has PD during/after platinum doublet chemotherapy for metastatic disease.
• Has confirmation that EGFR-, ALK-, or ROS1-directed therapy is not indicated as primary therapy.
• Has submitted pre-study imaging that confirmed evidence of PD following initiation of an anti-PD-1/PD-L1 inhibitor.
• Has at least 1 measurable lesion by computerized tomography (CT) or magnetic resonance imaging (MRI) per RECIST 1.1, as determined by the local site assessment.
• Has provided tumor tissue for PD-L1 biomarker analysis from an archival sample (defined as: from initial diagnosis of NSCLC and prior to receiving immunotherapy [antiPD-1/PD-L1], from the primary lesion or a metastatic lesion).
• Has provided prior to allocation tissue from a newly obtained formalin-fixed sample from a new biopsy (defined as: after completion of immunotherapy [anti-PD-1/PD-L1] and before receiving a randomization number), of a tumor lesion not previously irradiated.
• Has Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 within 7 days before the first dose of study intervention but before randomization.
• Has a life expectancy of at least 3 months.
• Male participants receiving pembrolizumab ± lenvatinib or lenvatinib must agree to refrain from donating sperm, and either 1) be abstinent from heterosexual intercourse; or 2) follow contraceptive guidance during the treatment period or 7 days after the last dose of lenvatinib. Male participants receiving docetaxel agree to adhere to the same conditions during the treatment period and for ≥180 days after the last dose of study treatment.
• Female participants must be not pregnant, not breastfeeding, and not be a woman of child-bearing potential (WOCBP). If a WOCBP, agrees to not donate eggs and either use contraception, or be abstinent from heterosexual intercourse during the treatment period and for ≥120 days after the last dose of pembrolizumab or 30 days after the last dose of lenvatinib, whichever occurs first. If a WOCBP receiving docetaxel, agrees to adhere to the same conditions during the treatment period and for ≥180 days after the last dose of study treatment.
• Has adequately controlled blood pressure (BP) with or without antihypertensive medications, defined as BP ≤150/90 mm Hg and no change in antihypertensive medications within 1 week before randomization.
• If participant received major surgery or radiation therapy of >30 Gy, they have recovered from the toxicity and/or complications from the intervention.
• Has adequate organ function.

Exclusion Criteria:

• Has received docetaxel as monotherapy or in combination with other therapies.
• Has received lenvatinib as monotherapy or in combination with an anti-PD-1/PD-L1 mAb.
• Has received: 1) radiotherapy within 2 weeks before the first dose of study treatment; or 2) lung radiation therapy >30 Gy within 6 months before the first dose of study treatment.
• Has received a live vaccine within 30 days before the first dose of study treatment.
• Has clinically significant hemoptysis or tumor bleeding within 2 weeks before the first dose of study treatment.
• Has radiographic evidence of intratumoral cavitation, encasement, or invasion of a major blood vessel.
• Has clinically significant cardiovascular impairment within 12 months of the first dose of study treatment.
• Has a history of a gastrointestinal condition or procedure that may affect oral absorption of study treatment.
• Has a pre-existing ≥Grade 3 gastrointestinal or non-gastrointestinal fistula.
• Is currently participating in a clinical trial and receiving study therapy or participated in a study of an investigational agent within 4 weeks of the first dose of study treatment.
• Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy or any other form of immunosuppressive therapy within 7 days before the first dose of study treatment.
• Has a known history of an additional malignancy, except if the participant has undergone potentially curative therapy with no evidence of disease recurrence for 3 years since initiation of that therapy.
• Has known active central nervous system metastases and/or carcinomatous meningitis.
• Has severe hypersensitivity to pembrolizumab and/or any of its excipients.
• Has a sensitivity to any of the excipients contained in lenvatinib and/or docetaxel.
• Has an active autoimmune disease that has required systemic treatment in the past 2 years.
• Has a history of (noninfectious) pneumonitis that required systemic steroids or current pneumonitis/interstitial lung disease.
• Has an active infection requiring systemic therapy.
• Has a known history of human immunodeficiency virus (HIV) infection.
• Has a known history of hepatitis B reactive or known active hepatitis C virus infection.
• Has active tuberculosis.
• Has a known psychiatric or substance abuse disorder that would interfere with the participant's ability to cooperate with the requirements of the study.
• Has a left ventricular ejection fraction (LVEF) below the institutional normal range.
• Has QT interval corrected with Fridericia's formula (QTcF) prolongation to >480 msec.
• Is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the study, starting with the screening visit through at least 120 days after the last dose of pembrolizumab or lenvatinib, or 180 days after the last dose of docetaxel.
• Has had an allogeneic tissue/solid organ transplant.