An Exploratory Study of Atezolizumab and Bevacizumab in Hepatocellular Carcinoma and Non-Small Cell Lung Cancer With Liver Metastases (INTEGRATE)

Inclusion Criteria: * Be willing and able to provide written informed consent. * Be ≥ 18 years of age on day of signing informed consent. * Have histologically or cytologically confirmed diagnosis of inoperable hepatocellular carcinoma (HCC) or non-squamous non-small cell lung cancer (NSCLC) with liver metastases with at least one measurable lesion. * NSCLC patients who were previously treated with chemotherapy or treatment naïve patients with a programmed death ligand-1 (PD-L1) tumor proportion score ≥50% or tumor cell score 3/immune cell score 3 are included. * NSCLC patients must be epidermal growth factor receptor (EGFR) and anaplastic lymphoma kinase (ALK) wild type. * HCC patients may be treatment naïve or treated with prior tyrosine kinase inhibitor(s). * Have a current liver function meeting Child Pugh Class A (5-6 points) in patients with HCC, with no encephalopathy or ascites. * Be willing to provide tumor tissue from a core biopsy of a tumor lesion (archival not acceptable). The subject must have a site of disease amenable to biopsy, and be a candidate for tumor biopsy. In addition, the subject must be willing to give blood for correlative studies, and have no contraindications to this. * Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) Performance Scale. * Have recovered (to ≤ grade 1) from prior toxicities related to previous treatments at the time of study enrollment, with the exception of alopecia or skin depigmentation. * Be tested for Hepatitis B-virus surface antigen (HBsAg) status. Patients may be included in the study if they have adequately controlled hepatitis B * Patients must be tested for hepatitis C virus (HCV) status. Subjects with chronic infection by HCV who are untreated are allowed on study. In addition, subjects with successful HCV treatment are allowed as long as 4 weeks have passed between completion of HCV therapy and start of study treatment. * Demonstrate adequate organ function. * Agrees to use use highly effective contraceptive methods, not donate egg or sperm, during study participation, and for at least 6 months after the last dose of study medications. * Life expectancy expected to be 3 months or greater. Exclusion Criteria: * Has received stereotactic radiotherapy within 4 weeks of trial commencement. For chemotherapy, tyrosine kinase inhibitors and palliative-dose radiotherapy, a 2 week washout is required. * Is currently participating and receiving experimental treatment as part of a clinical trial, or has participated in a study of an immune checkpoint inhibitor and received study therapy, or used an investigational device within 4 weeks of the first dose of treatment. * Inadequately controlled hypertension (defined as systolic blood pressure \[BP\] \> 150 mmHg and/or diastolic blood pressure \> 100 mmHg), based on an average of ≥ 3 BP readings on ≥ 2 sessions. Anti-hypertensive therapy to achieve these parameters is allowed. * History of hypertensive crises or hypertensive encephalopathy * Significant cardiovascular disease (such as New York Heart Association Class II or greater cardiac disease, myocardial infarction, or cerebrovascular accident within 3 months prior to initiation of study treatment), unstable arrhythmia, or unstable angina * Significant vascular disease (eg. aortic aneurysm requiring surgical repair or recent peripheral arterial thrombosis) within 6 months prior to randomization * History of Grade ≥ 4 venous thromboembolism. * History of Grade ≥ 2 hemoptysis (defined as ≥ 2.5 mL of bright red blood per episode) within 1 month prior to screening for HCC and within 3 months for NSCLC. * History or evidence of bleeding diathesis or significant coagulopathy at risk of bleeding (ie. In the absence of therapeutic anticoagulation) * Surgical procedure (including open biopsy, surgical resection, wound revision, or any other major surgery involving entry into a body cavity) or significant traumatic injury within 28 days prior to initiation of study treatment and wounds are fully healed, or anticipation of need for major surgical procedure during the course of the study. * Serious, non-healing or dehiscing wound, active ulcer, or untreated bone fracture. * Evidence of tumor invading or abutting major blood vessels. * History of abdominal fistula, gastrointestinal (GI) perforation, intra-abdominal abscess, or active GI bleeding within 6 months prior to randomization. * Serious, non-healing wound, active ulcer, or untreated bone fracture * Current or recent (\< 10 days prior to initiation of study treatment) use of aspirin (\> 325 mg/day) or treatment with dipyramidole, ticlopidine, clopidogrel (\> 75 mg/day) and cilostazol. * Current or recent (\< 10 days prior to initiation of study treatment) use of full-dose oral or parenteral anticoagulants or thrombolytic agents for therapeutic purpose * Has symptomatic, untreated or actively progressing central nervous system (CNS) metastases. Asymptomatic patients treated for CNS metastases may be eligible if they meet required criteria. * Uncontrolled tumor-related pain * Treatment with systemic immunostimulatory agents (including, but not limited to, interferon and interleukin 2 \[IL-2\]) within 4 weeks or 5 half-lives of the drug (whichever is longer) prior to initiation of study treatment. * Has had a previous allogeneic stem cell or solid organ transplant, a diagnosis of immunodeficiency, or is receiving systemic corticosteroid therapy or any other form of immunosuppressive therapy (eg. cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor \[TNF\]-α agents) within 7 days prior to the first dose of trial treatment, or anticipation of need for systemic immunosuppressive medication during study treatment. * Has histological or cytological diagnosis of fibrolamellar HCC, mixed cholangiocarcinoma or sarcomatoid HCC. * Untreated or incompletely treated esophageal and/or gastric varices with bleeding or high risk for bleeding * Has had a prior bleeding event due to esophageal and/or gastric varices within 6 months prior to initiation of study treatment. * History of allergic reactions or hypersensitivity attributed to compounds of similar chemical or biologic composition to either Atezolizumab or Bevacizumab. * Has had hepatic encephalopathy in the past 6 months, or has clinically apparent ascites at the time of study enrollment * History of idiopathic pulmonary fibrosis, organizing pneumonia (eg. bronchiolitis obliterans), drug-induced pneumonitis, or idiopathic pneumonitis, or evidence of active pneumonitis on screening chest computed tomography (CT) scan. * Has active Bacillus Tuberculosis (TB) * Has had prior treatment-related toxicity and not recovered (i.e. ≤ Grade 1 or at baseline) * Chronic daily treatment with a non-steroidal anti-inflammatory drug (NSAID) * Has a known history of prior clinically relevant invasive malignancy except if the subject has undergone curative-intent therapy with no evidence of disease recurrence for 2 years prior to study entry. Exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin, superficial bladder cancer, low-risk prostate cancer or in-situ cervical cancer. * Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g. thyroxine, insulin, or physiologic corticosteroid replacement therapy at a dose of ≤ 10 mg/day of prednisolone or equivalent) is not considered a form of systemic therapy. * Has a known history of, or any evidence of active, non-infectious pneumonitis. * Has an active infection requiring systemic oral or intravenous (IV) antibiotic therapy within 2 weeks prior to initiation of treatment. * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subjects participation for the full duration of the trial, or is not in the best interest of the subject to participate in the opinion of the treating investigator. * Has known psychiatric, substance abuse disorder, or any other condition that, in the opinion of the investigator, would interfere with cooperation with the requirements of the trial * Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through at least 6 months after the last dose of study drugs * Has received prior therapy with CD137 agonists or immune checkpoint blockade therapies including anti-cytotoxic T-lymphocyte associated protein 4 (CTLA4), anti-programmed death-1 (PD-1), anti-PD-L1, anti-programmed death ligand-2 (PD-L2) agent, or bevacizumab. * Has a known history of Human Immunodeficiency Virus (HIV) * Has received a live vaccine within 30 days of planned start of study therapy or anticipation of need for such a vaccine during atezolizumab treatment or within 5 months after the last dose of atezolizumab.