Ramucirumab and Atezolizumab After Progression on Any Immune Checkpoint Blocker in NSCLC

Inclusion Criteria: * Histologically or cytologically confirmed squamous or non-squamous non-small cell lung cancer. Patients with known EGFR or ALK mutations are eligible only if they have received at least one line of targeted therapy for these mutations. * Availability of archival biopsy tissue or willingness to undergo a "baseline" biopsy prior to initiation of the trial for biomarker analysis, including PD-L1 by IHC. Note: Results of PD-L1 testing are not required for enrollment. * Measurable disease defined as lesions that can be accurately measured in at least one dimension (longest diameter to be recorded) as ≥ 10 mm with CT scan, as ≥ 20 mm by chest x-ray, or ≥ 10 mm with calipers by clinical exam. * Prior use of an immune checkpoint blocker alone or in combination therapy. * At least 18 years of age. * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 1 * Normal bone marrow and organ function as defined below: * Absolute neutrophil count ≥ 1,500/cumm * Platelets ≥ 100,000/cumm * Hemoglobin ≥ 9.0 g/dL * Total bilirubin ≤ 1.5 x ULN * AST(SGOT)/ALT(SGPT) ≤ 3.0 x ULN or 5.0 x ULN in the setting of liver metastasis * Serum creatinine ≤ 1.5 x ULN or CrCl ≥ 40 mL/min. if serum creatinine is \>1.5 times the ULN, a 24-hour urine collection to calculate creatinine clearance must be performed * Adequate coagulation function as defined by: * INR ≤ 1.5 * PTT/aPTT \< 1.5 x ULN * Note: Patients on full-dose anticoagulation must be on a stable dose (minimum duration 14 days) of oral anticoagulant or low molecular weight heparin (LMWH). If receiving warfarin, the patient must have an INR ≤3.0. For heparin and LMWH there should be no active bleeding (that is, no bleeding within 14 days prior to first dose of protocol therapy) or pathological condition present that carries a high risk of bleeding (for example, tumor involving major vessels or known varices). * Urinary protein ≤ 1+ on dipstick or routine urinalysis; if urine dipstick or routine analysis is ≥ 2+, a 24-hour urine collection for protein must demonstrate \< 1000 mg of protein in 24 hours to allow participation * Women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control, abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while participating in this study, she must inform her treating physician immediately. * Ability to understand and willingness to sign an IRB approved written informed consent document (or that of legally authorized representative, if applicable). Exclusion Criteria: * Treatment with cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor \[anti-TNF\] agents) within 2 weeks prior to Cycle 1, Day 1. \*Note: Patients who have received acute, low-dose, systemic immunosuppressant medications (e.g., a one-time dose of dexamethasone for nausea or premedication for contrast dye allergy) are eligible. The use of inhaled corticosteroids for chronic obstructive pulmonary disease (COPD) and mineralocorticoids (e.g., fludrocortisone) for patients with orthostatic hypotension or adrenocortical insufficiency is allowed. * A history of other malignancy ≤ 3 years previous with the exception of patients with a negligible risk of metastasis or death and with expected curative outcome (such as adequately treated carcinoma in situ of the cervix, basal or squamous cell skin cancer, localized prostate cancer treated surgically with curative intent, or ductal carcinoma in situ treated surgically with curative intent) or undergoing active surveillance per SOC management (e.g., Rai Stage 0 chronic lymphocytic leukemia, prostate cancer with Gleason score ≤ 6 and prostate-specific antigen (PSA ≤ 10 ng/mL, etc.). * Currently receiving any other investigational agents. * Symptomatic or untreated asymptomatic brain metastases. Patients with treated brain metastases are eligible if they are clinically stable with regard to neurologic function, off steroids after cranial irradiation (whole brain radiation therapy, focal radiation therapy, and stereotactic radiosurgery) ending at least 2 weeks prior to randomization, or after surgical resection performed at least 28 days prior to randomization. The patient may have no evidence of Grade ≥1 CNS hemorrhage based on pretreatment MRI or IV contrast CT scan (performed within 21 days before randomization). * A history of allergic reactions attributed to compounds of similar chemical or biologic composition to atezolizumab, ramucirumab, any other immune checkpoint blockade, chimeric or humanized antibodies, fusion proteins, or other agents used in the study. * Receiving chronic antiplatelet therapy, including aspirin, nonsteroidal anti-inflammatory drugs (NSAIDs, including ibuprofen, naproxen, and others), dipyridamole or clopidogrel, or similar agents. Once-daily aspirin use (maximum dose 325 mg/day) is permitted. * Arterial or venous thromboembolic event, including but not limited to myocardial infarction, transient ischemic attack, cerebrovascular accident, or unstable angina, within 6 months prior to enrollment. * Uncontrolled or poorly controlled hypertension (\> 160 mmHg systolic or \> 100 mmHg diastolic for \> 4 weeks) despite standard medical management. * Gastrointestinal perforation, and/or fistula, or risk factors for perforation within 6 months prior to enrollment. * Grade 3 or 4 gastrointestinal bleeding within 3 months prior to enrollment. * History of autoimmune disease, including but not limited to systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjögren's syndrome, Bell's palsy, Guillain-Barré syndrome, multiple sclerosis, autoimmune thyroid disease, vasculitis, or glomerulonephritis. \*Note: Patients with a history of autoimmune hypothyroidism on a stable dose of thyroid replacement hormone are eligible. Patients with controlled type 1 diabetes mellitus on a stable insulin regimen are eligible. * History of idiopathic pulmonary fibrosis, pneumonitis (including drug-induced), organizing pneumonia (i.e., bronchiolitis obliterans, cryptogenic organizing pneumonia, etc.), or evidence of active pneumonitis on screening chest CT scan. * Hemoptysis (defined as bright red blood or ≥ ½ teaspoon) within 2 months prior to Cycle 1 Day 1 or with radiographic evidence of intratumor cavitation or radiologically documented evidence of major blood vessel invasion or encasement by cancer. * Serious or non-healing would, ulcer, or bone fracture within 28 days prior to Cycle 1 Day 1. * Undergone major surgery within 28 days prior to Cycle 1 Day 1, or minor surgery/subcutaneous venous access device placement within 7 days prior to Cycle 1 Day 1, or has elective or planned major surgery to be performed during the course of the clinical trial. * Known clinically significant liver disease, including active viral, alcoholic, or other hepatitis, cirrhosis at a level of Child-Pug B or worse, cirrhosis (any degree) with a history of hepatic encephalopathy or clinically meaningful ascites resulting from cirrhosis (defined as ascites from cirrhosis requiring diuretics or paracentesis), fatty liver, and inherited liver disease. --Active hepatitis B virus (HBV) or hepatitis C virus (HCV) infection (defined as, HBV surface antigen (HBsAg) positive and HBV core antibody (HbcAb) positive with reflex positive HBV DNA. Note: Patients with past or resolved hepatitis B infection (defined as having a negative HBsAg test and a positive HBcAb test or treated HCV with negative HCV RNA are eligible. * Known HIV-positivity. * Active tuberculosis. * Administration of a live, attenuated influenza vaccine within 4 weeks before Cycle 1 Day 1 or at any time during the study. * Severe infections within 2 weeks prior to Cycle 1 Day 1, including but not limited to hospitalization for complications of infection, bacteremia, or severe pneumonia. Received oral or intravenous (IV) antibiotics within 2 weeks prior to Cycle 1 Day 1. Note: Patients receiving prophylactic antibiotics (e.g., for prevention of a urinary tract infection or chronic obstructive pulmonary disease) are eligible. * History of deep venous thrombosis, pulmonary embolism, or any other significant thromboembolism (venous port or catheter thrombosis or superficial venous thrombosis are not considered "significant") during the 3 months prior to Cycle 1 Day 1. * Pregnant and/or breastfeeding. Women of childbearing potential must have a negative serum pregnancy test within 7 days of study entry.