A Study to Assess Adverse Events and Change in Disease Activity of Intravenously (IV) Infused ABBV-324 in Adult Participants With Hepatocellular Cancer (HCC) or Squamous-Cell Non-Small Cell Lung Cancer (LUSC)

Inclusion Criteria: * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * Hepatocellular cancer (HCC) only: Child-Pugh A classification within 7 days before Cycle 1, Day 1 dosing. * Laboratory values meeting the criteria outlined in the protocol. * QT interval corrected for heart rate (QTc) \< 470 msec (using Fridericia's correction), no Grade 3 arrythmia, and no other clinically significant cardiac abnormalities. * Measurable disease per RECIST version 1.1. * Part 1 and Part 2 - participants with HCC meeting the following disease activity criteria: * Locally advanced or metastatic and/or unresectable HCC with diagnosis confirmed by histology or cytology. Participants with fibrolamellar HCC, sarcomatoid HCC, or mixed cholangiocarcinoma/HCC are not eligible to enroll. * Disease that is not amenable to surgical and/or locoregional therapies, or progressive disease after surgical and/or locoregional therapies. For participants who progressed after locoregional therapy for HCC, locoregional therapy must have been completed \>= 28 days prior to baseline scan for the current study. * Part 1: Failure of at least 1 prior systemic treatment for HCC. * Part 2: Failure of at least 1 prior systemic treatment consisting of an immune checkpoint inhibitor (CPI) containing regimen for HCC, including but not limited to, atezolizumab in combination with bevacizumab or tremelimumab in combination with durvalumab. Note: Participants who have received prior lenvatinib will not be eligible for Part 2. * Part 1 only - participants with squamous-cell non-small cell lung cancer (LUSC) meeting the following disease activity criteria: * Advanced or metastatic LUSC that is not amenable to surgical resection. * Must have failed at least 1 prior line of therapy that included at least platinum-based chemotherapy and an immune CPI, and/or an appropriate targeted therapy (if applicable), or is not suitable for other approved therapeutic options that have demonstrated clinical benefit at the judgment of the investigator. Participants should have no more than 2 lines of prior cytotoxic chemotherapy excluding neoadjuvant and/or adjuvant. Participants who are intolerant of standard therapy are eligible. Exclusion Criteria: * Unresolved clinically significant adverse events (AEs) \> Grade 1 from prior anticancer therapy except for alopecia. * Untreated brain or meningeal metastases (i.e., participants with history of metastases are eligible provided they do not require ongoing steroid treatment for cerebral edema and have shown clinical and radiographic stability for at least 14 days after definitive therapy). Participants may continue with antiepileptic therapy if required. * History of interstitial lung disease (ILD) or pneumonitis that required treatment with systemic steroids, nor any evidence of active ILD or pneumonitis on screening chest computed tomography (CT) scan. * History of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans), drug-induced pneumonitis, or idiopathic pneumonitis. * History of clinically significant, intercurrent lung-specific illnesses including, but not limited to: * Underlying pulmonary disorder (i.e., pulmonary emboli within 3 months of the study enrollment, severe asthma, severe COPD, restrictive lung disease, pleural effusion, dependence on supplemental oxygen, etc.). * Any autoimmune, connective tissue or inflammatory disorders with documented or suspicious pulmonary involvement at Screening. * Must have discontinued anticancer therapy with antineoplastic intent including chemotherapy, radiation therapy, immunotherapy, biologic, or any investigational therapy within 14 days or 5 half lives of the drug (whichever is shorter) prior to the first dose of ABBV-324. Palliative radiation therapy for bone, skin or subcutaneous metastases with 10 fractions or less is permitted and not participant to a washout period.