• Age ≥ 18 years

• Confirmed recurrent or metastatic non-small cell carcinoma of the lung of any histology without curative options

• Measurable disease based on RECIST v1.1

• Patients must have received standard of care chemotherapy and/or immunotherapy. No limits to prior lines of therapy. Prior PD-1 and/or PD-L1 directed therapies are permitted

• Patients with adenocarcinoma and known actionable mutations with Food and Drug Administration (FDA) approved treatment options must have received all approved and standard of care treatment options (i.e. osimertinib for epidermal growth factor receptor (EGFR), alectinib for anaplastic lymphoma kinase (ALK), etc.). Mutational testing is not required for patients with squamous cell non-small cell lung carcinoma

• Eastern Cooperative Oncology Group (ECOG) performance status of 0-2

• Absolute neutrophil count (ANC) ≥ 1,500 /mcL without granulocyte colony-stimulating factor support

• Platelet count ≥ 100,000 /uL without transfusion

• Hemoglobin ≥ 90 g/L (9 g/dL) patients may be transfused to meet this criterion

• Measured or calculated creatinine clearance (calculated using the Cockcroft-Gault formula) ≥ 60 mL/min for subject with creatinine levels ≤ 1.5 x institutional upper limit of normal (ULN)

• Serum total bilirubin ≤ 1.5 x ULN with the following exception:

‣ Patients with known Gilbert disease: serum bilirubin ≤ 3 x ULN

• Direct bilirubin ≤ ULN for subjects with total bilirubin levels \> 1.5 ULN

• Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT)(serum glutamic pyruvic transaminase \[SGPT\]) ≤ 2.5 x ULN with the following exceptions:

‣ Patients with documented liver metastases: AST and ALT ≤ 5 x ULN

⁃ Both values must be in the specified range

• Alkaline phosphatase (ALP) ≤ 2.5 x ULN with the following exceptions:

‣ Patients with documented liver or bone metastases: ALP ≤ 5 x ULN

• Albumin ≥ 2.5 g/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

• Anticipated life expectancy of ≥ 3 months

• Willing to comply with study procedures

• Female subject of childbearing potential will have a serum pregnancy test at screening. Urine pregnancy tests will be performed at specified subsequent visits. If a urine pregnancy test is positive, it must be confirmed by a serum pregnancy test

• For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods, and agreement to refrain from donating eggs, as defined below:

‣ Women must remain abstinent or use contraceptive methods with a failure rate of \< 1% per year during the treatment period and for 5 months after the final dose of atezolizumab and 24 months after the final dose of vismodegib. Women must refrain from donating eggs during this same period

⁃ A woman is considered to be of childbearing potential if she is postmenarchal, has not reached a postmenopausal state (≥ 12 continuous months of amenorrhea with no identified cause other than menopause), and has not undergone surgical sterilization (removal of ovaries and/or uterus). The definition of childbearing potential may be adapted for alignment with local guidelines or requirement

⁃ Examples of contraceptive methods with a failure rate of \< 1% per year include bilateral tubal ligation, male sterilization, hormonal contraceptives that inhibit ovulation, hormone-releasing intrauterine devices, and copper intrauterine devices

⁃ The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not adequate methods of contraception

• For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive measures, and agreement to refrain from donating sperm, for 5 months from last atezolizumab dose and 24 months after the final dose of vismodegib, as defined below:

‣ With a female partner of childbearing potential or pregnant female partner, men must remain abstinent or use a condom during the treatment period and, for 5 months from last atezolizumab dose and 24 months after the final dose of vismodegib to avoid exposing the embryo. Men must refrain from donating sperm during this same period

⁃ The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not adequate methods of preventing drug exposure

• Be willing and able to understand and sign the written informed consent document

• Availability of a recent formalin-fixed, paraffin-embedded (FFPE) tumor tissue block. A recently obtained archival FFPE tumor tissue block (if an FFPE tissue block cannot be provided, 15 unstained slides (10 minimum) will be acceptable) from a primary or metastatic tumor resection or biopsy can be provided if it was obtained within 1 year of trial screening

• Be willing to provide tissue from an on-treatment fine needle aspiration (FNA) or core biopsy of a tumor lesion. Subjects must consent to on-treatment biopsy prior to initiation of clinical trial, however subjects for whom newly-obtained samples cannot be provided (e.g. inaccessible or subject safety concern) may still continue on study

• Negative HIV test at screening with the following exception: patients with a positive HIV test at screening are eligible provided they are stable on anti-retroviral therapy, have a CD4 count \> 200/uL, and have an undetectable viral load

• Negative total hepatitis B core antibody (HBcAb) test at screening. For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated

• Negative hepatitis C virus (HCV) antibody test at screening, or positive HCV antibody test followed by a negative HCV ribonucleic acid (RNA) test at screening

‣ The HCV RNA test must be performed for patients who have a positive HCV antibody test