Inclusion Criteria:  Participants must have c-Met overexpressing non-small cell lung cancer (NSCLC) as assessed by an AbbVie designated immunohistochemistry (IHC) laboratory. Archival or fresh tumor material must be submitted for assessment of c-Met levels during the Pre-Screening period. Tumor material from the primary tumor site and/or metastatic sites are allowed. A histologically documented non-squamous cell NSCLC that is locally advanced or metastatic. A known epidermal growth factor receptor (EGFR) activating mutation status. Actionable alterations in genes other than EGFR . Measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1. An Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 to 1.  Have received no more than 1 line of prior systemic cytotoxic chemotherapy in the locally advanced or metastatic setting.  Neoadjuvant and adjuvant systemic cytotoxic chemotherapy will count as a prior line for eligibility purposes if progression occurred within 6 months of the end of therapy.  Have progressed on at least 1 line of prior therapy for locally advanced/metastatic NSCLC:  Participants WITHOUT an actionable gene alteration: must have progressed on (or be considered ineligible for) platinum-based chemotherapy and immune checkpoint inhibitor (as monotherapy or in combination with chemotherapy).  Participants WITH an actionable gene alteration for which immune checkpoint inhibitor therapy is not standard of care (e.g., anaplastic lymphoma kinase [ALK] translocation): must have progressed on (or be considered ineligible for) anti-cancer therapy targeting driver gene alterations and platinum-based chemotherapy.  Participants with actionable gene alterations for which immune checkpoint inhibitor is standard of care must have also progressed on (or be considered ineligible for) immune checkpoint inhibitor (as monotherapy or in combination with chemotherapy). Must be considered appropriate for docetaxel therapy based on the assessment of the treating physician.  Participants with metastases to the central nervous system (CNS) are eligible only after definitive therapy (such as surgery or radiotherapy) is provided and:  There is no evidence of progression of CNS metastases at least 4 weeks after definitive therapy. They are asymptomatic and off or on a stable or reducing dose of systemic steroids and/or anticonvulsants for at least 2 weeks prior to first dose of telisotuzumab vedotin.  Exclusion Criteria:  Participants with adenosquamous histology. Actionable epidermal growth factor receptor (EGFR) activating mutations. Participants who have received prior c-Met-targeted antibodies. Participants who have received prior docetaxel therapy.  A history of other malignancies except:  Malignancy treated with curative intent and with no known active disease present for >=2 years before the first dose of study drug and felt to be at low risk for recurrence by investigator. Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease. Adequately treated carcinoma in situ without current evidence of disease. A history of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans), drug-induced pneumonitis, or idiopathic pneumonitis, or evidence of active pneumonitis on screening chest computed tomography (CT) scan. A history of prior radiation pneumonitis in the radiation field (fibrosis) is permitted. Unresolved clinically significant adverse event (AE) >= Grade 2 from prior anticancer therapy, except for alopecia or anemia. Major surgery within 21 days prior to the first dose of telisotuzumab vedotin. Clinically significant condition(s) as listed in the protocol.