Atezolizumab and Cobimetinib in Treating Patients With Metastatic, Recurrent, or Refractory Non-small Cell Lung Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed metastatic or recurrent non-small cell lung cancer (any histology is permitted) * Presence of a mutation in KRAS as detected by a Clinical Laboratory Improvement Act (CLIA)-approved assay is required for patients enrolled in cohort 1; central validation is not required for enrollment * Absence of a mutation in KRAS (KRAS wild type) is required for patients enrolled in cohort 2; central validation is not required for enrollment but KRAS mutation status must be known, regardless of histology * Patients must have primary resistance to anti-PD-1 or anti-PD-L1 therapy, given as monotherapy or in combination with other agents; patients must have experienced progressive disease within 6 months (180 days) of initiating treatment with a PD-1/PD-L1 inhibitor * Anti-PD-1 or anti-PD-L1 therapy does not need to be the most recent therapy prior to study enrollment * Patients with a sensitizing alteration in EGFR, ALK or ROS1 are eligible provided they have experienced disease progression or intolerance to treatment with an approved EGFR, ALK or ROS1 inhibitor, respectively; patients who have received investigational inhibitors may be eligible following discussion with the study principal investigator (PI) * Patients must have disease amenable to core biopsy and be willing to undergo the required research biopsies * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm (\>= 2 cm) by chest x-ray or as \>= 10 mm (\>= 1 cm) with CT scan, MRI, or calipers by clinical exam * Age \>= 18 years * Because no dosing or adverse event data are currently available on the use of atezolizumab in combination with cobimetinib in patients \< 18 years of age, children are excluded from this study, but will be eligible for future pediatric trials * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Leukocytes \>= 2,500/mcL * Absolute neutrophil count \>= 1,000/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 8 g/dL * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (however, patients with known Gilbert disease who have serum bilirubin level =\< 3 x upper limit of normal \[ULN\] may be enrolled) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x ULN (AST and/or ALT =\< 5 x ULN for patients with liver involvement) * Alkaline phosphatase =\< 2.5 x ULN (=\< 5 x ULN for patients with documented liver involvement or bone metastases) * Creatinine clearance \>= 30 mL/min/1.73 m\^2 by Cockcroft-Gault * Institutional normalized ratio (INR) and partial thromboplastin time (aPTT) =\< 1.5 x ULN; (this applies only to patients who do not receive therapeutic anticoagulation; patients receiving therapeutic anticoagulation, such as low-molecular-weight heparin or warfarin, should be on a stable dose) * Administration of atezolizumab or cobimetinib may have an adverse effect on pregnancy and poses a risk to the human fetus, including embryo-lethality; women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 5 months (150 days) after the last dose of study agent; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial Exclusion Criteria: * Patients who have not recovered from clinically significant adverse events (other than alopecia) due to prior anti-cancer therapy * Treatment with any investigational agent within 4 weeks prior to cycle 1, day 1 * Treatment with systemic immunosuppressive medications (including, but not limited to, prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor \[anti-TNF\] agents) within 2 weeks prior to cycle 1, day 1 * 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 symptomatic central nervous system (CNS) metastases are excluded * 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 within 28 days prior to cycle 1, day 1 * 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 within 28 days prior to cycle 1, day 1 * Screening CNS radiographic study \>= 4 weeks from completion of radiotherapy and \>= 2 weeks from discontinuation of corticosteroids * Has a known concurrent malignancy that is expected to require active treatment within two years, or may interfere with the interpretation of the efficacy and safety outcomes of this study in the opinion of the treating investigator; superficial bladder cancer, non-melanoma skin cancers, or low grade prostate cancer not requiring therapy should not exclude participation in this trial * Known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies * History of allergic reactions attributed to compounds of similar chemical or biologic composition to atezolizumab or cobimetinib * History of congenital long QT syndrome or corrected QT interval (QTc) by Fridericia Formula \> 450 msec within 28 days of cycle 1, day 1 * Cardiac ejection fraction below institutional lower limit of normal (LLN) or below 50%, whichever is lower, as determined by echocardiogram or multigated acquisition (MUGA) scan within 4 weeks of cycle 1, day 1 * History of or evidence of retinal pathology on ophthalmologic examination that is considered a risk factor for neurosensory retinal detachment, central serous chorioretinopathy, retinal vein occlusion (RVO), or neovascular macular degeneration * Any grade 3 or above hemorrhage or bleeding event within 4 weeks prior to initiation of study treatment * History of stroke, reversible ischemic neurological defect, or transient ischemic attack within 6 months prior to initiation of study treatment * Patients receiving any medications or substances that are strong or moderate inhibitors or inducers of CYP3A4 enzymes are ineligible; these include St. John's wort or hyperforin (potent CYP3A4 enzyme inducer) and grapefruit juice (potent cytochrome P450 CYP3A4 enzyme inhibitor); because the lists of these agents are constantly changing, it is important to regularly consult medical reference texts such as the Physicians' Desk Reference may also provide this information; as part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product * Known clinically significant liver disease, including active viral, alcoholic, or other hepatitis; cirrhosis; fatty liver; and inherited liver disease * 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, autoimmune hemolytic anemia, Wegener's granulomatosis, Sjogren's syndrome, Bell's palsy, Guillain-Barre syndrome, multiple sclerosis, vasculitis, or glomerulonephritis * Patients with a history of autoimmune hypothyroidism on a stable dose of thyroid replacement hormone may be eligible * Patients with controlled type 1 diabetes mellitus on a stable insulin regimen may be 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; history of radiation pneumonitis in the radiation field (fibrosis) is permitted * Any significant active infection requiring treatment within 14 days prior to cycle 1, day 1 * Major surgical procedure within 28 days prior to cycle 1, day 1 or anticipation of need for a major surgical procedure during the course of the study * Administration of a live, attenuated vaccine within 4 weeks before cycle 1, day 1 or anticipation that such a live, attenuated vaccine will be required during the study and up to 5 months after the last dose of atezolizumab * Influenza vaccination should be given during influenza season only (approximately October to March); patients must not receive live, attenuated influenza vaccine within 4 weeks prior to cycle 1, day 1 or at any time during the study * Uncontrolled pleural or pericardial effusion or ascites requiring recurrent drainage procedures * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, active tuberculosis (TB), 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 because both atezolizumab and cobimetinib are expected to cause fetal harm if used during pregnancy; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with cobimetinib or atezolizumab, breastfeeding should be discontinued if the mother is treated with either therapy; these potential risks may also apply to other agents used in this study * Inability or unwillingness to swallow pills * History of malabsorption syndrome or other condition that would interfere with enteral absorption