Nivolumab With or Without Ipilimumab or Chemotherapy in Treating Patients With Previously Untreated Stage I-IIIA Non-small Cell Lung Cancer

Inclusion Criteria: * Histologically or cytologically confirmed previously untreated non-small cell lung cancer. If a diagnostic biopsy is available, a pre-treatment biopsy is not required. Patients with a suspected lung cancer are eligible, but pathology must be confirmed prior to initiating treatment on study. Neuroendocrine carcinomas are not eligible. Carcinomas with neuroendocrine differentiation are eligible * Patients with stage IA or stage IB \< 4 cm (according to American Joint Committee on Cancer \[AJCC\] 7th edition) are eligible for randomization into arms A and B only. Patients with stage IB \>= 4 cm, IIA, IIB, or IIIA disease (according to AJCC 7th edition) are eligible for randomization into arms A, and B, and for enrollment into arms C and D * Patients with stage IIIA must not have more than one mediastinal lymph node station involved by tumor * All patients must have lymph node evaluation of contralateral stations 2 and/or 4 to exclude N3 disease * The patient must be a suitable candidate for surgery, in the opinion of the treating physician * Signed and dated written informed consent must be provided by the patient prior to admission to the study in accordance with International Conference on Harmonization-Good Clinical Practice (ICH-GCP) guidelines and to the local legislation * Eastern Cooperative Oncology Group (ECOG) performance status score 0-1 * Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L * Hemoglobin \>= 8.0 g/dL * Platelets \>= 100 x 10\^9/L * Total bilirubin =\< 1.5 x upper limit of normal (ULN) (except subjects with Gilbert syndrome who can have total bilirubin \< 3.0 mg/dL) * Creatinine =\< 1.5 x ULN or calculated creatinine clearance \>= 50 mL/min using Cockcroft-Gault formula for creatinine clearance calculation OR 24-hour urine creatinine clearance \>= 50 mL/min Exclusion Criteria: * Prior systemic therapy or radiation therapy for treatment of the current lung cancer * Currently receiving cancer therapy (chemotherapy, radiation therapy, immunotherapy, or biologic therapy) or investigational anti-cancer drug * Pregnant or lactating female: Women of childbearing potential (WOCB) must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin \[HCG\]) within 72 hours prior to the start of nivolumab; Women of childbearing potential is defined as any female who has experienced menarche and who has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy) or who is not postmenopausal. Menopause is defined clinically as 12 months of amenorrhea in a woman over 45 in the absence of other biological or physiological causes * Unwillingness or inability to follow the procedures required in the protocol * Patients with pre-existing sensorineural hearing impairment/loss or newly diagnosed as documented by an audiology assessment performed prior to study enrollment may not be eligible for cisplatin and may be dispositioned to carboplatin, as determined by the treating physician. * Patients with a history of severe hypersensitivity reaction to taxotere and or polysorbate 80 must be excluded * Any serious or uncontrolled medical disorder that, in the opinion of the investigator, may increase the risk associated with study participation or study drug administration, impair the ability of the subject to receive protocol therapy, or interfere with the interpretation of study results * Subjects with active, known or suspected autoimmune disease. Subjects with vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll * Subjects with a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration. Inhaled or topical steroids and adrenal replacement doses \> 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease. Subjects are permitted to use topical, ocular, intra-articular, intranasal, and inhalational corticosteroids (with minimal systemic absorption). Physiologic replacement doses of systemic corticosteroids are permitted, even if \> 10 mg/day prednisone equivalents. A brief course of corticosteroids for prophylaxis (eg, contrast dye allergy) or for treatment of non-autoimmune conditions (eg, delayed-type hypersensitivity reaction caused by contact allergen) is permitted * Prior treatment with an anti-PD-1, anti-PD-L1 or anti-CTLA-4 antibody * Known positive test for hepatitis B virus surface antigen (HBV sAg) or hepatitis C virus ribonucleic acid indicating acute or chronic infection * Known history of testing positive for human immunodeficiency virus or known acquired immunodeficiency syndrome * History of severe hypersensitivity reaction to any monoclonal antibody and/or to study drug components * Serious illness or concomitant non-oncological disease such as neurologic, psychiatric, infectious disease or laboratory abnormality that may increase the risk associated with study participation or study drug administration and in the judgment of the investigator would make the patient inappropriate for entry into the study * Patients who are sexually active, with preserved reproductive capacity, and unwilling to use a medically acceptable method of contraception (e.g. such as implants, injectables, combined oral contraceptives, some intrauterine devices or vasectomized partner for participating females, condoms for participating males) during and after the trial * Women of child bearing potential (WOCBP) should use an adequate method to avoid pregnancy for 23 weeks after the last dose of investigational drug(s); Men who are sexually active with WOCBP must use any contraceptive method with a failure rate of less than 1% per year; Men receiving nivolumab and who are sexually active with WOCBP will be instructed to adhere to contraception for a period of 31 weeks after the last dose of investigational product; Women who are not of childbearing potential as well as azoospermic men do not require contraception * Psychological, familial, sociological or geographical factors potentially hampering compliance with the study protocol and follow-up schedule