Pembrolizumab, Paclitaxel, Carboplatin, and Radiation Therapy in Treating Patients With Stage II-IIIB Non-Small Cell Lung Cancer

Inclusion Criteria: * Written informed consent and Health Insurance Portability and Accountability Act (HIPPA) authorization for release of personal health information * Subjects with any kind of non-small cell lung carcinoma (NSCLC) histology documented by histology or cytology from bronchial brushing or washing, or needle aspiration of a defined lesion but not from sputum cytology alone * Must have American Joint Committee on Cancer (AJCC) 7th edition (ed) inoperable stage II disease requiring chemoradiation therapy or stage IIIA or IIIB NSCLC based on appropriate staging studies including brain magnetic resonance imaging (MRI) or head computed tomography (CT), CT chest, and fluorodeoxyglucose (FDG) positron emission tomography (PET)/CT scan * Be willing to provide tissue from a newly obtained core or excisional biopsy of a tumor lesion; newly-obtained is defined as a specimen obtained up to 8 weeks (56 days) before initiation of treatment on day 1; subjects for whom newly-obtained samples cannot be provided (e.g. inaccessible or subject safety concern) may submit an archived specimen only upon agreement from the sponsor or may undergo fine needle aspiration * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 within 14 days before registration for protocol therapy * Absolute neutrophil count (ANC) \>= 1,500/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L without transfusion or erythropoietin (EPO) dependency (within 7 days of assessment) * Serum creatinine OR measured or calculated creatinine clearance (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance rate \[CrCl\]) =\< 1.5 X upper limit of normal (ULN) OR \>= 60 mL/min for subject with creatinine levels \> 1.5 X institutional ULN * Serum total bilirubin =\< 1.5 X ULN OR direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 ULN * 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 liver metastases * Albumin \>= 2.5 mg/dL * 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 * Forced expiratory volume \>= 1.0 L or \>= 40% of predicted with or without bronchodilators by pulmonary function testing * Women 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 * Women 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 * Have measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 Exclusion Criteria: * Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 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 before the first dose of trial treatment * Has a known history of active Bacillus tuberculosis (TB) * Hypersensitivity to pembrolizumab or any of its excipients * Has had a prior anti-cancer monoclonal antibody (mAb) within 4 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, or radiation 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 * 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 basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis; subjects with previously treated brain metastases may not participate * 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 known history of, or any evidence of 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-PD-1, anti-PD-L1, or anti- programmed cell death 1 ligand 2 (PD-L2) agent * Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies) * Has known active hepatitis B (e.g., hepatitis B virus surface antigen \[HBsAg\] reactive) or hepatitis C (HCV) (e.g., HCV ribonucleic acid \[RNA\] \[qualitative\] is detected) * Has received a live vaccine within 30 days of planned start of study therapy * Pleural effusion that cannot be controlled despite appropriate interventions * History of allergy or hypersensitivity to any component of the treatment * No active second cancers