Testing the Effects of MK-3475 (Pembrolizumab) With or Without the Usual Chemotherapy Treatment for Patients 70 Years of Age and Older With Advanced Non-small Cell Lung Cancer

This study evaluates the side effects of pembrolizumab with or without chemotherapy in treating patients with stage IV non-small cell lung cancer that has come back after a period of improvement (recurrent) and may have spread from where it first started to nearby tissue, lymph nodes, or distant parts of the body (advanced). Immunotherapy with monoclonal antibodies, such as pembrolizumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Drugs used in chemotherapy, such as pemetrexed and carboplatin, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving pembrolizumab with or without chemotherapy may shrink the tumor in older patients with non-small cell lung cancer.

Inclusion Criteria: * Documentation of Disease: Histologic or cytologic diagnosis of non-small cell lung cancer (adenocarcinoma). Stage IV or recurrent metastatic non-small cell lung cancer. No planned initiation of definitive (potentially curative) concurrent chemo-radiation * Planning to begin MK-3475 (pembrolizumab) treatment within 14 days of registration, with or without combination chemotherapy. Treating physician considers pembrolizumab as appropriate and plans to proceed with one of the following treatment schedules: * MK-3475 (pembrolizumab) 200 mg IV flat dose every 21 days or 400 mg IV flat dose every 42 days. * MK-3475 (pembrolizumab) 200 mg IV/ 400 mg IV + carboplatin area under the curve (AUC) = 5 + pemetrexed 500 mg/m\^2 (20% chemotherapy dose reduction is permitted per the discretion of the treating physician) * Patients will be ineligible if they are post-organ transplantation, or are receiving ongoing immunosuppression treatment. Patients will be ineligible if they have an active autoimmune disease that has required systemic treatment in past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs) \* Note: Replacement therapy (i.e., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. Patients who require inhaled corticosteroids would not be excluded from the study. Patients with vitiligo or resolved childhood asthma/atopy would not be excluded from the study. Patients who require local steroid injections (for example, a steroid injection to a joint) would not be excluded from the study. * Prior adjuvant therapy is allowed and must have been completed at least 6 months prior to registration * No planned radiation or other cancer treatment in the 3 months following registration * No untreated brain metastases. Patients must be off oral and IV corticosteroids for this condition and asymptomatic at registration * Age \>= 70 years of age * Absolute neutrophil count (ANC) \>= 1500/mm\^3 (1.5 x 10\^9/L) * Platelet count: \>= 100,000/mm\^3 (100 x 10\^9/L) * Calculated creatinine clearance \>= 30 mL/min\* for patients enrolled to pembrolizumab alone and \> 45 mL/min for patients enrolled to chemotherapy + pembrolizumab \* Calculated using the Cockcroft-Gault formula * Total bilirubin =\< 1.5 upper limit of normal (ULN) (\< 3 ULN if Gilbert's disease) * Aspartate aminotransferase (AST) and/or alanine aminotransferase (ALT) =\< 3 x ULN (=\< 5.0 x ULN if liver metastases present) * Alkaline phosphatase =\< 2.5 x ULN (=\< 5 x ULN if bone or liver metastases present) Language: Patients must be able to speak and comprehend English in order to complete the mandatory patient-completed measures