Anetumab Ravtansine and Atezolizumab in Treating Participants With Advanced Non-small Cell Lung Cancer

Inclusion Criteria: * PRE REGISTRATION ? INCLUSION CRITERIA: Ability to understand and the willingness to sign a written informed consent document * PRE REGISTRATION ? INCLUSION CRITERIA: Patient has disease amenable to biopsy if the archival tissue sample is unavailable; note: Archive sample must not be older than 12 months * REGISTRATION ? INCLUSION CRITERIA * Phase I only: Diagnosis of advanced/metastatic NSCLC for which no standard treatment option; Phase II only: Advanced NSCLC patients who have received at least 1 platinum-based systemic chemotherapy regimen * Patients with tumors having actionable genomic alterations should have received prior therapy with Food and Drug Administration (FDA) approved agents targeting these aberrations (ie EGFR, ALK, ROS1, BRAF V600E) * Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 * Phase II only: Must have at least one measurable lesion as defined by Response Evaluation Criteria in Solid Tumors (RECIST) criteria * Ability to understand and the willingness to sign a written informed consent document * Histological or cytologically confirmed NSCLC that shows moderate or stronger mesothelin expression in 30% of tumor cells by a companion assay; MSLN expression score using Ventana immunohistochemistry (IHC) SP74 assay; Phase I only: In addition 5- 30% tumor cells and 1, 2, or 3+ MSLN score; Phase II only: 30% tumor cells and either 2+/3+ * Life expectancy of \>= 12 weeks * Absolute neutrophil count \>= 1.5 ? 10\^9/L =\< 14 days prior to registration * Platelets \>= 100 ? 10\^9/L =\< 14 days prior to registration * Hemoglobin \>= 9 g/dL =\< 14 days prior to registration * Potassium \>= lower limit of normal (LLN) range for the institution =\< 14 days prior to registration * NOTE: Supplementation may be given before the first dose of study medication * Calcium \>= LLN (corrected for serum albumin, if albumin abnormal) =\< 14 days prior to registration * NOTE: Supplementation may be given before the first dose of study medication * Magnesium \>= LLN =\< 14 days prior to registration * NOTE: Supplementation may be given before the first dose of study medication * Sodium \>= LLN =\< 14 days prior to registration * NOTE: Supplementation may be given before the first dose of study medication * Phosphorus \>= LLN =\< 14 days prior to registration * NOTE: Supplementation may be given before the first dose of study medication * International normalized ratio (INR) =\< 1.5 =\< 14 days prior to registration * Serum creatinine =\< 1.5 mg/dL or creatinine clearance \>= 50 mL/min (calculated by Cockcroft Gault equation) =\< 14 days prior to registration * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x ULN or =\< 5 x upper limits of normal (ULN) if liver metastases are present =\< 14 days prior to registration * Total bilirubin =\< 1.5 x ULN =\< 14 days prior to registration * Standard 12-lead electrocardiogram (ECG) with the following parameters at screening (defined as the mean of the triplicate ECGs): * QT corrected by Fridericia's formula (QTcF) interval at screening \< 450msec (using Fridericia?s correction) * Negative pregnancy test performed =\< 7 days prior to registration (women of childbearing potential only) * Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study) * Willing to provide blood samples for correlative research purposes Exclusion Criteria: * REGISTRATION ? EXCLUSION CRITERIA * Prior treatment with anti-PD-1, or anti-PD-L1 therapeutic antibody or pathway-targeting agents * Note: * Patients who have received prior treatment with anti-CTLA-4 may be enrolled, provided the following requirements are met: * Minimum of 12 weeks from the first dose of anti-CTLA-4 and \> 6 weeks from the last dose * No history of severe immune-related adverse effects from anti-CTLA-4 (National Cancer Institute \[NCI\] Common Terminology Criteria for Adverse Events \[CTCAE\] grade 3 and 4) * More than one prior taxane regimen at any stage of the disease under study (?taxane? refers to paclitaxel, docetaxel, abraxane and cabazitaxel); adjuvant and/or neoadjuvant treatments are considered together as one prior regimen * Treatment with any other investigational agent or investigational device within 4 weeks prior to registration (or within five half-lives of the investigational product, whichever is longer); patients must be \>= 2 weeks since any investigational agent administered as part of a phase 0 study (also referred to as an ?early phase I study? or ?pre phase I study? where a sub- therapeutic dose of drug is administered) at the coordinating center principal investigator (PI)?s discretion, and should have recovered to eligibility levels from any toxicities * Treatment with systemic immunostimulatory agents (including, but not limited to, interferon-alpha or interleukin-2) within 6 weeks or five half-lives of the drug (whichever is shorter) prior to registration * Received radiotherapy =\< 4 weeks or limited field radiation for palliation =\< 2 weeks prior to registration, and who has not recovered to grade 1 or better from related side effects of such therapy (exceptions include alopecia) and/or in whom \>= 25 percent (%) of the bone marrow was irradiated * Patients who have a previous or concurrent cancer that is distinct in primary site or histology from the cancer being evaluated in this study, except * Cervical carcinoma in situ, non-melanoma skin cancer, superficial noninvasive bladder tumors, ductal carcinoma in situ (DCIS) or any previous cancer curatively treated \>3 years before the start of anetumab ravtansine * Treatment with systemic immunosuppressive medications (including, but not limited to, prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor \[anti-TNF\] agents) =\< 2 weeks prior to registration * Note: * Patients who have received acute, low dose, systemic immunosuppressant medications (e.g., a one-time dose of dexamethasone for nausea) may be enrolled * The use of inhaled corticosteroids and mineralocorticoids (e.g., fludrocortisone) for patients with orthostatic hypotension or adrenocortical insufficiency is allowed * Patients with known primary central nervous system (CNS) malignancy or symptomatic CNS metastases are excluded, with the following exceptions * Patients with asymptomatic untreated CNS disease may be enrolled, provided all of the following criteria are met: * Evaluable or measurable disease outside the CNS * No metastases to brain stem, midbrain, pons, medulla, cerebellum, or within 10 mm of the optic apparatus (optic nerves and chiasm) * No history of intracranial hemorrhage or spinal cord hemorrhage * No ongoing requirement for dexamethasone for CNS disease; patients on a stable dose of anticonvulsants are permitted * No neurosurgical resection or brain biopsy =\< 28 days prior to registration * Patients with asymptomatic treated CNS metastases may be enrolled, provided all the criteria listed above are met as well as the following: * Radiographic demonstration of improvement upon the completion of CNS-directed therapy and no evidence of interim progression between the completion of CNS-directed therapy and the screening radiographic study * No stereotactic radiation or whole-brain radiation =\< 28 days prior to registration * Screening CNS radiographic study \>= 4 weeks from completion of radiotherapy and \>= 2 weeks from discontinuation of corticosteroids * History of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins * Patients who have a history or current evidence of bleeding disorder, i.e., any hemorrhage/bleeding event of CTCAE grade \>= 2, =\< 28 days prior to registration * History or current evidence of uncontrolled cardiovascular disease including, but not limited to, the following conditions: * Congestive heart failure of New York Heart Association (NYHA) class III or IV * Unstable angina (symptoms of angina at rest) or new-onset angina =\< 6 months before the start of anetumab ravtansine * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with atezolizumab * Patients on supraphysiologic doses of steroids or use of such =\< 6weeks prior to registration * Known clinically significant liver disease, including active viral, alcoholic, or other hepatitis; cirrhosis; fatty liver; and inherited liver disease * Note: * Patients with past or resolved hepatitis B infection (defined as having a negative hepatitis B surface antigen \[HBsAg\] test and a positive anti-HBc \[antibody to hepatitis B core antigen\] antibody test) are eligible * Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA) * History or risk 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, Sjogren?s syndrome, Bell?s palsy, Guillain-Barre 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 * Patients with eczema, psoriasis, lichen simplex chronicus of vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis would be excluded) are permitted provided that they meet the following conditions: * Patients with psoriasis must have a baseline ophthalmologic exam to rule out ocular manifestations * Rash must cover less than 10% of body surface area (BSA) * Disease is well controlled at baseline and only requiring low potency topical steroids (e.g., hydrocortisone 2.5%, hydrocortisone butyrate 0.1%, flucinolone 0.01%, desonide 0.05%, aclometasone dipropionate 0.05%) * No acute exacerbations of underlying condition within the last 12 months (not requiring psoralen plus ultraviolet A radiation \[PUVA\], methotrexate, retinoids, biologic agents, oral calcineurin inhibitors; high potency or oral steroids) * 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 computed tomography (CT) scan; note: History of radiation pneumonitis in the radiation field (fibrosis) is permitted * Severe infections =\< 4 weeks prior to registration, including, but not limited to, hospitalization for complications of infection, bacteremia, or severe pneumonia * Signs or symptoms of infection =\< 2 weeks prior to registration * Major surgical procedure =\< 28 days prior to registration or anticipation of need for a major surgical procedure during the course of the study * Patients with corneal epitheliopathy or any eye disorder that may predispose the patients to this condition as judged by an ophthalmologist * Note: Low grades of superficial punctate keratitis, within the range seen in the normal population, should not lead to the exclusion of the patient * Non-healing serious wound, ulcer, or bone fracture unrelated to the primary tumor * Previous assignment to treatment during this study; patients permanently withdrawn from study participation will not be allowed to re-enter the study * Substance abuse, psychological, or social conditions that may interfere with the patient's participation in the study or evaluation of the study results