Inclusion Criteria:

          -  Patients must have histologically or cytologically confirmed metastatic or recurrent
             non-small cell lung cancer

               -  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

               -  If, and only if, cohort 1 is positive (at least 1 out of up to 24 patients
                  experience a confirmed durable response, lasting at least 6 months), then cohort
                  2 will open. This can occur prior to full enrollment to 24 patients. Absence of a
                  mutation in KRAS (KRAS wild type) is required for patients enrolled in cohort 2.
                  Central validation is not required for enrollment

          -  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 experienced progressive
             disease within 6 months (180 days) of initiating treatment with a PD-1/PD-L1 inhibitor

          -  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 computed tomography (CT) scan, magnetic resonance
             imaging (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) > 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, autoimmune thyroid disease, 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