Phase 2 DoceRamPem for Patients With Metastatic or Recurrent NSCLC Who Progressed on Platinum-Doublet and PD-1/PD-L1 Blockade

Inclusion Criteria: * Histologically confirmed diagnosis of non-small cell lung cancer * Patients must have progressed on a platinum-based chemotherapy and any of the Food and Drug Administration (FDA)-approved PD-1 or PD-L1 immune checkpoint inhibitors, either given sequentially or in combination * A male participant must agree to use a contraception during the treatment period plus an additional 120 days after the last dose of study treatment and refrain from donating sperm during this period * A female participant is eligible to participate if she is not pregnant, not breastfeeding, and at least one of the following conditions applies: * Not a woman of childbearing potential (WOCBP) OR * A WOCBP who agrees to follow the contraceptive guidance during the treatment period and for at least 120 days plus 30 days (a menstruation cycle) after the last dose of study treatment * The participant (or legally acceptable representative if applicable) provides written informed consent for the trial * Has measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST) 1.1. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions * Has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1 * Life expectancy \> 12 weeks as determined by the investigator * Absolute neutrophil count (ANC) ≥ 1500/uL (collected within 10 days prior to the start of study treatment) * Platelets ≥ 100 000/uL (collected within 10 days prior to the start of study treatment) * Hemoglobin ≥ 9.0 g/dL or ≥ 5.6 mmol/L (collected within 10 days prior to the start of study treatment) * Criteria must be met without erythropoietin dependency and without packed red blood cell (pRBC) transfusion within last 2 weeks * Creatinine ≤ 1.5 x upper limit of normal (ULN) OR measured or calculated creatinine clearance (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance \[CrCl\]) ≥ 30 mL/min for participant with creatinine levels \> 1.5 x institutional ULN (collected within 10 days prior to the start of study treatment) * Creatinine clearance (CrCl) should be calculated per institutional standard * Total bilirubin ≤ 1.5 x ULN OR direct bilirubin ≤ ULN for participants with total bilirubin levels \> 1.5 x ULN (collected within 10 days prior to the start of study treatment) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) ≤ 2.5 x ULN (≤ 5 x ULN for participants with liver metastases) (collected within 10 days prior to the start of study treatment * Palliative radiotherapy (to bone or soft tissue lesions) must be completed \> 1 week prior to start of study drug (exception: palliative radiotherapy for pain may be used any time prior to first dose) * Clinically significant toxic effect(s) of the most recent prior anti-cancer therapy must be grade 1 or resolved (except alopecia and sensory neuropathy); patients with grade 2 adrenal insufficiency related to prior anti-cancer therapy (defined as requiring medical intervention, such as concomitant steroids) or grade 2 hypothyroidism (defined as requiring hormone replacement therapy) may be enrolled provided that clinical symptoms are adequately controlled and the daily dose is 10 mg or less of prednisone or equivalent. If the patient received major surgery or radiation therapy of \> 30 Gy, they must have recovered from the toxicity and/or complications from the intervention * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better Exclusion Criteria: * A WOCBP with a positive urine pregnancy test within 72 hours prior of the planned treatment on day 1 of each cycle. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Patients have prior exposure to docetaxel or ramucirumab * Patients with proteinuria of ≥ 2+ on dipsticks or urine protein/creatinine ratio of \> 1 g/24-hour * Has received prior systemic anti-cancer therapy including investigational agents within 4 weeks or 5 times the half-life time, whichever is shorter \[could consider shorter interval for kinase inhibitors or other short half-life drugs\] prior to allocation * Note: Participants must have recovered from all adverse events (AEs) due to previous therapies to grade ≤ 1 or baseline. Participants with grade ≤ 2 neuropathy may be eligible * Note: If participant received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study treatment * Has received prior radiotherapy within 1 week of start of study treatment. Participants must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. A 1-week washout is permitted for palliative radiation (≤ 2 weeks of radiotherapy) to non-central nervous system (CNS) disease * Has received a live vaccine within 30 days prior to the first dose of study drug. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, bacillus Calmette-Guerin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (eg, FluMist) are live attenuated vaccines and are not allowed * Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to the first dose of study treatment * Note: Participants who have entered the follow-up phase of an investigational study may participate as long as it has been 4 weeks after the last dose of the previous investigational agent * Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug * Patients with symptomatic brain metastasis (patients with treated brain metastasis without symptoms and not requiring steroid are allowed to participate) * Has severe hypersensitivity (grade ≥ 3) to pembrolizumab and/or any of its excipients * Patients with uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, significant cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Patients with significant cardiovascular disease (e.g., myocardial infarction, arterial thromboembolism, cerebrovascular thromboembolism) within 6 months prior to start of study therapy; angina requiring therapy; symptomatic peripheral vascular disease; New York Heart Association class 3 or 4 congestive heart failure; or uncontrolled grade ≥ 3 hypertension (diastolic blood pressure ≥ 100 mmHg or systolic blood pressure ≥ 160 mmHg) despite antihypertensive therapy * Patients with any major hemorrhage or thromboembolic events within 3 months prior to start on this study * Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment * Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis or established interstitial lung disease * Patients who had prior history of immune-related adverse event (irAE) that required treatment with steroids and permanent immune checkpoint inhibitor (ICI) discontinuation per National Comprehensive Cancer Network (NCCN) guidelines * Has an active infection requiring systemic therapy * Has a known history of Human Immunodeficiency Virus (HIV). Note: no HIV testing is required unless mandated by local health authority * Has a known history of Hepatitis B (defined as Hepatitis B surface antigen \[HBsAg\] reactive) or known active Hepatitis C virus (defined as HCV RNA is detected) infection. Note: no testing for Hepatitis B and Hepatitis C is required unless mandated by local health authority * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the study, starting with the screening visit through 120 days after the last dose of trial treatment