The main purpose of the study is to assess whether the study drug, LY4066434, is safe and tolerable when administered to participants with locally advanced or metastatic solid tumors with certain KRAS mutations. LY4066434 will be given alone or in combination with other treatments. The study will have 2 parts: monotherapy dose escalation and dose optimization. The study is expected to last up to approximately 5 years.

Inclusion Criteria:

• Have evidence of KRAS G12C, G12D, G12V, G12A, G12S, or G13D mutation in tumor tissue or circulating tumor DNA
• Histological or cytologically proven diagnosis of a locally advanced, unresectable, and/or metastatic solid tumor cancer
• Have measurable disease per RECIST 1.1
• Have an ECOG performance status of ≤1
• Must not be pregnant and/or planning to breastfeed during the trial or within 180 days of the last dose of trial intervention
• Must be able to swallow tablets
• Participants with asymptomatic or treated CNS disease may be eligible

Exclusion Criteria:

• Have known active CNS metastases and/or carcinomatous meningitis
• Have any unresolved toxicities from prior therapy greater than NCI CTCAE Version 5.0 Grade 1 at the time of starting trial treatment, except for alopecia, hearing loss, peripheral neuropathy and ongoing endocrinopathies controlled on appropriate replacement therapy
• Have significant cardiovascular disease defined as unstable angina or acute coronary syndrome, history of myocardial infarction, known left ventricular ejection fraction or heart failure, uncontrolled or symptomatic arrhythmias.
• Have known active hepatitis B virus (HBV), hepatitis C virus (HCV) or untreated HIV infection
• Have other active malignancy unless in remission with life expectancy greater than 2 years.
• Have active uncontrolled systemic bacterial, viral, fungal, or parasitic infection
• Have history of non-infectious pneumonitis/interstitial lung disease that received steroids or has current clinically significant pneumonitis/interstitial lung disease