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.