Key inclusion criteria:  Signed informed consent form (ICF) and able to comply with study requirements Histologically and/or cytologically confirmed advanced solid tumor types such as one of following: Non-small cell lung cancer (NSCLC), Squamous Cell Carcinoma of the Head and Neck (SCCHN), Colorectal Cancer (UC), or Renal Cell Carcinoma (RCC). At least 1 measurable lesion per RECIST version 1.1 Tumor tissue (approximately 10 unstained slides) for central laboratory assessment of pd-l1 status for the NSCLC cohort during the screening period, and for retrospective analysis of other exploratory biomarkers related to response and resistance for NSCLC, SCCHN, UC, or GC cohorts in a BeiGene designated central or test laboratory. ECOG performance status ≤ 1  Key exclusion criteria:  For the NSCLC cohort, active leptomeningeal disease or uncontrolled, untreated brain metastasis will be excluded. For other cohorts than NSCLC, patients with known leptomeningeal disease or brain metastasis will be excluded. Prior therapy with lenvatinib or an anti-pd-1, anti-pd-l1, anti-pd-l2 or any other antibody or drug specifically targeting t-cell costimulation or checkpoint pathways History of interstitial lung disease, noninfectious pneumonitis, or uncontrolled lung diseases including but not limited to pulmonary fibrosis, acute lung diseases, etc. Inability to swallow capsules or disease/procedure significantly affecting gastrointestinal function, such as malabsorption syndrome, resection of the stomach or small bowel, bariatric surgery procedures, symptomatic inflammatory bowel disease, or partial or complete bowel obstruction Have clinically significant bleeding (such as ctcae ≥ grade 2) within 21 days before first dose  NOTE: OTHER PROTOCOL DEFINED INCLUSION/EXCLUSION CRITERIA MAY APPLY