Inclusion Criteria:
* Histologically or cytologically confirmed small cell lung cancer (SCLC) that is relapsed or refractory following at least 1 prior platinum-containing chemotherapy, but no more than 3 total prior lines of therapy, and with no curative therapy available.
* Measurable disease, defined as at least 1 tumor lesion greater than or equal to 10 mm in the longest diameter or a lymph node greater than or equal to 15 mm in short axis measurement assessed by computed tomography (CT) scan, according to Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1.
* Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.
* Minimum life expectancy of at least 12 weeks.
* Recovery to at least Grade 1 of any clinically significant toxicity (excluding alopecia) prior to initiation of study drug administration.
* Adequate hematologic, hepatic, neurologic, and renal function.
* All participants in Part B and Part C will be required to have tumor tissue that tests positive for target expression.
* Sponsor may elect for confirmed SCLC tumor tissue to test positive for target expression for Parts A and D participants as well.
* Last dose of any prior anticancer therapy \>= 4 weeks before the first dose of study drug.
Additional Inclusion Criteria for Study Part B and Part C:
* SCLC tumor tissue that tests positive for seizure-related homolog 6 (SEZ6) by immunohistochemistry (IHC).
Exclusion Criteria:
* History of confirmed or suspected liver cirrhosis, hepatic veno-occlusive disease (VOD), sinusoidal obstruction syndrome (SOS), alcohol dependence, or ongoing excessive alcohol use.
* Prior history of allogeneic or autologous stem cell transplantation.
* Documented history of stroke or clinically significant cardiac disease as described in the protocol within 6 months prior to the first dose of study drug.
* History of cardiac conduction abnormalities as described in the protocol.
* Recent or ongoing serious infection, as described in the protocol.
* Active SARS-CoV-2 infection.
* Prior or concomitant malignancies with some exceptions, as described in the protocol.
* Any significant medical or psychiatric condition, including any suggested by Screening laboratory findings, that in the opinion of the Investigator or Sponsor may place the participant at undue risk from the study treatment, interfere with interpretation of study results, or compromise ability to comply with protocol requirements.
* Participants with a history of hypersensitivity to the active ingredients or any excipients of study drugs (ABBV-011 or budigalimab \[ABBV-181\]) will be excluded.
Additional Exclusion Criteria for Part C:
* History of inflammatory bowel disease.
* Peripheral neuropathy Grade 2 with pain, or Grade 3 or higher.
* Body weight less than 35 kilograms.
* Active pneumonitis or interstitial lung disease (ILD) or a history of pneumonitis/ILD requiring treatment with steroids.
* Participants previously treated with an anti PD-1/PD-L1 targeting agent must meet additional criteria described in the protocol.
* Participant is judged by the Investigator to have evidence of ongoing hemolysis.
* Immunosuppressive use with exceptions as per protocol.
* Participants who have received a live vaccine within 30 days of start of study treatment.
* Active autoimmune disease with exceptions as indicated in the protocol.
* History of primary immunodeficiency, solid organ transplantation, or previous clinical diagnosis of tuberculosis.
* Participants with a history of Stevens-Johnson syndrome (SJS), toxic epidermal necrolysis (TEN), or drug reaction with eosinophilia and systemic symptoms (DRESS).
Additional exclusion criteria for Japanese and Korean participants:
\- Participants with a history of interstitial lung disease (pneumonitis) or current interstitial lung disease (pneumonitis).
