Inclusion Criteria:
* Have locally advanced or metastatic non-small cell lung cancer (NSCLC).
* Have c-Met+ NSCLC as assessed by an AbbVie designated immunohistochemistry (IHC) laboratory. Participant must submit archival or fresh tumor material for assessment of c-Met levels during the prescreening period. Tumor material from the primary tumor site and/or metastatic sites are allowed. If archival tissue is negative for c-Met overexpression, subject can submit fresh biopsy material for reassessment of c-Met expression.
* Histologically documented non-squamous epidermal growth factor receptor (EGFR) wild type NSCLC (site documented EGFR status). Of note, subjects with other actionable mutations are eligible as long as EGFR status is known and all other eligibility criteria are met. As of Protocol Version 11, Stage 1 is complete and Stage 2 is enrolling participants with non-squamous EGFR wild type NSCLC only.
* Must have received no more than 2 lines of prior systemic therapy (including no more than 1 line of systemic cytotoxic chemotherapy) in the locally advanced or metastatic setting.
* Multiple lines of tyrosine kinase inhibitors (TKIs) targeting the same tyrosine kinase (TK) count as 1 line of therapy for the purposes of this eligibility criterion.
* Progressed on systemic cytotoxic therapy (or are ineligible for systemic cytotoxic chemotherapy) and an immune checkpoint inhibitor (as monotherapy or in combination with systemic cytotoxic chemotherapy, or ineligible), and prior anticancer therapies targeting driver gene alterations (if applicable).
* Have an Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 to 1.
* Treatment with any therapies within the noted time intervals is excluded prior to the first dose of telisotuzumab vedotin as noted in the protocol.
* Metastases to the central nervous system (CNS) are eligible only after definitive therapy (such as surgery or radiotherapy) is provided within the protocol.
Exclusion Criteria:
* Have received radiation therapy to the lungs \< 6 months prior to the first dose of telisotuzumab vedotin.
* Have received any live vaccine within 30 days of the first dose of investigational product.
* Has adenosquamous histology.
* Have a history of other malignancies except those noted within the protocol.
* Have a history of interstitial lung disease (ILD) or pneumonitis that required treatment with systemic steroids.
* Have any evidence of pulmonary fibrosis on screening imaging assessment or any history of pneumonitis or ILD within 3 months of the planned first dose of the study drug (Except for Sites in Ireland). For imaging findings deemed clinically insignificant by the treating physician, subject may be eligible after discussion with and approval from the AbbVie medical monitor.
* For Sites in Ireland Only: Must not have any evidence of pulmonary fibrosis on screening imaging assessment or any history of pneumonitis or ILD. For imaging findings deemed clinically insignificant by the treating physician, subject may be eligible after discussion with and approval from the AbbVie medical monitor.
* Have a clinically significant condition(s) as noted in the protocol.
* Have unresolved clinically significant adverse events of Grade \>= 2 from prior anticancer therapy, except for alopecia or anemia.
* Have had major surgery within 21 days prior to the first dose of telisotuzumab vedotin.
* For Sites in France and Czech Republic Only: Have the following:
* Known human immunodeficiency virus (HIV) infection. Note: HIV testing is not required for eligibility for this protocol unless mandated by local regulatory authority or ethics committee/institutional review board.
* Active hepatitis B virus (HBV) infection, defined by hepatitis B surface antigen (HBsAg) positivity or HBV DNA \>= 500 IU/mL. In participants with known HBV infection, the presence of active infection must be tested locally. If HBV status is unknown, it must be tested locally at screening.
* Active hepatitis C virus (HCV) infection, defined by HCV ribonucleic acid (RNA) positivity. Participants cured of HCV infection may be included in the study. In participants with known HCV infection, the presence of active infection must be tested locally. If HCV status is unknown, it must be tested locally at screening.
* Uncontrolled autoimmune disease.
