Efficacy and Safety of Pembrolizumab (MK-3475) With Lenvatinib (E7080/MK-7902) vs. Docetaxel in Participants With Metastatic Non-Small Cell Lung Cancer (NSCLC) and Progressive Disease (PD) After Platinum Doublet Chemotherapy and Immunotherapy (MK-7902-008/E7080-G000-316/LEAP-008)

Inclusion Criteria:

* Has a histologically or cytologically confirmed diagnosis of metastatic squamous or nonsquamous Non-Small Cell Lung Cancer (NSCLC) -Stage IV: M1a, M1b, M1c.
* Has progressive disease (PD) on treatment with one prior anti-programmed cell death 1 (PD-1)/programmed cell death ligand 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 (documentation of absence of tumor-activating EGFR mutations \[eg, DEL19 or L858R\], and absence of ALK and ROS1 gene rearrangements OR presence of a K-ras mutation).
* 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 Response Evaluation Criteria in Solid Tumors (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 ≥90 days after the last dose of study treatment.
* Female participants must not be pregnant, not be 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 last. If a WOCBP receiving docetaxel, agrees to adhere to the same conditions during the treatment period and for ≥30 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.
* 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 90 days (male participants) or 30 days (for female participants) after the last dose of docetaxel.
* Has had an allogeneic tissue/solid organ transplant.