Pembrolizumab and Concurrent Chemoradiotherapy or Radiation Therapy in Treating Patients With Small Cell Lung Cancer

Inclusion Criteria: * Be willing and able to provide written informed consent/assent for the trial * Have a performance status of 0 or 1 or 2 on the Eastern Cooperative Oncology Group (ECOG) performance scale * Absolute neutrophil count (ANC) \>= 1,500/mcL (performed within 10 days of treatment initiation) * Platelets \>= 100,000/mcL (performed within 10 days of treatment initiation) * Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L (performed within 10 days of treatment initiation) * Serum creatinine or measured or calculated creatinine clearance (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance \[CrCl\]) =\< 1.5 X upper limit of normal (ULN) or \>= 60 mL/min for subject with creatinine levels \> 1.5 X institutional ULN (creatinine clearance should be calculated per institutional standard) (performed within 10 days of treatment initiation) * Serum total bilirubin =\< 1.5 X ULN or direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 ULN (performed within 10 days of treatment initiation) * Aspartate aminotransferase (AST) serum glutamic oxaloacetic transaminase (SGOT) and alanine aminotransferase (ALT) serum glutamate pyruvate transaminase (SGPT) =\< 2.5 X ULN or =\< 5 X ULN for subjects with metastatic malignant neoplasm in the liver (liver metastases) (performed within 10 days of treatment initiation) * International normalized ratio (INR) or prothrombin time (PT) =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants, activated partial thromboplastin time (aPTT) =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants (performed within 10 days of treatment initiation) * Female subjects of childbearing potential should have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication; if the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Female subjects of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication; subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year * Male subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy * Histologic diagnosis of either limited stage SCLC (LS-SCLC), or extensive stage SCLC (ES-SCLC) or neuroendocrine tumor Exclusion Criteria: * Is currently participating in or has participated in a study of an investigational agent (except glutamine) or using an investigational device within 2 weeks of the first dose of treatment * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment; with the exception of physiologic steroid replacement * Has had a prior monoclonal antibody within 2 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier * Has had prior chemotherapy, targeted small molecule therapy, within 2 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to a previously administered agent; prior radiation does not require a washout period; note: subjects with =\< grade 2 neuropathy are an exception to this criterion and may qualify for the study; note: if subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy * Has a known additional malignancy that is progressing or requires active treatment; exceptions include skin basal cell carcinoma (basal cell carcinoma of the skin), skin squamous cell carcinoma (squamous cell carcinoma of the skin), or in situ cervical cancer that has undergone potentially curative therapy * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis; subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment * Has an active autoimmune disease requiring systemic treatment within the past 3 months or a documented history of clinically severe autoimmune disease, or a syndrome that requires systemic steroids or immunosuppressive agents; subjects with vitiligo or resolved childhood asthma/atopy would be an exception to this rule; subjects that require intermittent use of bronchodilators or local steroid injections would not be excluded from the study; subjects with hypothyroidism stable on hormone replacement or Sjogren's syndrome will not be excluded from the study * Has evidence of interstitial lung disease or active, non-infectious pneumonitis * Has an active infection requiring systemic therapy * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator * 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 trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment * Has received prior therapy with an anti-programmed cell death-1 (PD-1), anti-programmed cell death-ligand 1 (PD-L1), anti-programmed cell death 1 ligand 2 (PD-L2), anti-cluster of differentiation (CD)137 * Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies) * Has known active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus ribonucleic acid \[HCV RNA\] \[qualitative\] is detected) * Has received a live vaccine within 30 days prior to the first dose of trial treatment