Inclusion Criteria:
* Participant must have advanced Non-Small Cell Lung Cancer (NSCLC) that is not amenable to surgical resection or other approved therapeutic options that have demonstrated clinical benefit.
* Participant has an Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 to 2. For Monotherapy Expansion Cohort, participant must have ECOG Performance Status of 0 or 1.
* Participant must have measurable disease per Response Evaluation Criteria In Solid Tumors (RECIST) version 1.1.
* Participant has archived diagnostic formalin-fixed paraffin embedded (FFPE) tumor tissue confirmed available for analyses.
* Participant has adequate bone marrow, renal, and hepatic function.
* Women of childbearing potential must have a negative serum pregnancy test at baseline.
* Participants in the combination therapy arms A and D must be eligible to receive erlotinib, or nivolumab per most locally approved labeling, or at the discretion of the Investigator.
* Participants in the combination therapy Arm E must satisfy following criteria.
* Participant must have metastatic/locally advanced nonsquamous NSCLC with documented Epidermal Growth Factor Receptor (EGFR) mutation(s) del19 or L858R, with or without T790M mutation, and none of the EGFR mutations known to be resistant to osimertinib.
* Participant must have received at least 1 but no more than 2 prior regimens, one of which must have contained osimertinib. Participant must have had disease progression while on osimertinib. Only 1 prior regimen may have contained chemotherapy. Consecutive EGFR TKIs will count as 1 regimen
* Participant must have available post-progression tumor tissue for central c-Met immunohistochemistry (IHC) testing.
* Participant has adequate bone marrow function.
* Participants in the Monotherapy Expansion Cohort must satisfy following criteria.
* Participant must have locally advanced or metastatic, non-squamous, EGFR wild type, c-Met+ NSCLC. Participants must not have adenosquamous histology.
* Participant 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.
* Participant must have progressed on systemic cytotoxic chemotherapy (or are ineligible for systemic cytotoxic chemotherapy) and an immune checkpoint inhibitor (as monotherapy or in combination with systemic cytotoxic chemotherapy, or ineligible for an immune checkpoint inhibitor), and prior anti-cancer therapies targeting driver gene alterations (if applicable).
* Participant should not have received prior c-Met-targeted antibody-based therapies.
Exclusion Criteria:
* Participant has received radiation therapy to the lung \< 6 months prior to the first dose of ABBV-399.
* Participant has received anticancer therapy including chemotherapy, immunotherapy, biologic, or any investigational therapy within a period of 21 days or herbal therapy within 7 days prior to the first dose of ABBV-399.
* Participant has uncontrolled metastases to the central nervous system (CNS) based on head CT or MRI. Participants with brain metastases may be eligible 2-4 weeks after definitive therapy to all known sites of CNS disease provided they are asymptomatic and either off or on a non-increasing dose (in last 2 weeks) of systemic steroids and not on anticonvulsants for seizure activity directly related to progressive CNS metastases.
* Participant has history of interstitial lung disease (ILD) or pneumonitis that required treatment with systemic steroids.
* Participant has evidence of pulmonary fibrosis on screening imaging assessment or any history of pneumonitis or interstitial lung disease (ILD) within 3 months of the planned first dose of the study drug.
* Participant has unresolved clinically significant adverse events \>= Grade 2 from prior anticancer therapy, except for alopecia or anemia.
* Participant has had major surgery within 21 days prior to the first dose of ABBV-399.
* Participant has a clinically significant condition(s) described in the protocol.
* History of major immunologic reaction to any Immunoglobulin G (IgG) containing agent.
* Participant has any medical condition which in the opinion of the Investigator or Medical Monitor places the participant at an unacceptably high risk for toxicities.
* Participant is a lactating or pregnant female.
* Participant with known active COVID-19 infection, subjects with signs/symptoms associated with COVID-19 infection or known exposure to a confirmed case of COVID-19 infection during 14 days prior to Screening must be screen failed and may only rescreen after they have recovered from COVID-19 and they are no longer considered contagious, per investigator assessment.
* Participants enrolled on the combination therapy phase must satisfy the above exclusion criteria and also the following:
* Participants may not receive ABBV-399 in combination with osimertinib, erlotinib or nivolumab if they have any medical condition which in the opinion of the Investigator places the participant at an unacceptably high risk for toxicities from the combination.
* Participants may not receive nivolumab if they have:
* Active autoimmune disease with exceptions of vitiligo, type I diabetes mellitus, hypothyroidism and psoriasis.
* Used systemic corticosteroids (\> 10 mg daily prednisone or equivalent) or other immunosuppressive medications within 14 days of study drug administration, with exception of inhaled, locally injected or topical steroids.
* Known immunosuppressive disease, for example human immunodeficiency virus infection or history of bone marrow transplant or chronic lymphocytic leukemia.
* Participants may not be enrolled into the osimertinib Combination Therapy Arm E if they have the following:
* History of hypersensitivity to active or inactive excipients of osimertinib.
* History of osimertinib dose reduction.
* Refractory nausea and vomiting, chronic gastrointestinal diseases, inability to swallow the formulated product, or previous significant bowel resection that would preclude adequate absorption of osimertinib.
* Any of the following cardiac criteria: a) Mean resting corrected QT interval (QTc) \> 470 ms; b) Any clinically important abnormalities in rhythm, conduction, or morphology of resting ECG, e.g., complete left bundle branch block, second- or third-degree heart block, PR interval \> 250 ms; c) Any factors that increase the risk of QTc prolongation or risk of arrhythmic events such as heart failure, hypokalemia, congenital long QT syndrome, or any concomitant medication known to prolong the QT interval.
