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HCC is a common cancer worldwide and a leading cause of cancer-related death. Lung cancer is the most frequently diagnosed cancer in the world, and the leading cause of cancer deaths. The purpose of this study is to assess adverse events and change in disease activity when ABBV-324 is given to adult participants to treat hepatocellular cancer (HCC) or squamous-cell non-small cell lung cancer (LUSC). ABBV-324 is an investigational drug being developed for the treatment of HCC and LUSC. Study doctors put the participants in groups called arms. Each arm receives ABBV-324 alone (monotherapy) or a comparator drug, lenvatinib followed by a safety follow-up period. Approximately 232 HCC or LUSC will be enrolled in the study in approximately 45 sites worldwide. In the dose escalation stage participants will be treated with increasing intravenous (IV) doses of ABBV-324 until the dose reached is tolerable and expected to be efficacious. In the dose optimization stage participants will receive ABBV-324, or a comparator of oral lenvatinib. The study will run for a duration of approximately 6.5 years. There may be higher treatment burden for participants in this trial compared to their standard of care. Participants will attend regular visits during the study at an approved institution (hospital or clinic). The effect of the treatment will be frequently checked by medical assessments, blood tests, questionnaires and side effects.

Drug: Lenvatinib

This research is designed to determine if experimental treatment with AZD9793, a T cell-engaging antibody that targets GPC3, is safe, tolerable and has anti-cancer activity in patients with advanced or metastatic solid tumours which are GPC3+.

Drug: AZD9793 Subcutaneous (SC) monotherapy