Have known active central nervous system (CNS) metastases or carcinomatous meningitis
- Individuals with asymptomatic untreated brain metastases may participate with:
  - No acute neurological symptoms requiring urgent CNS-directed therapy (radiation or surgery)
  - No requirements for corticosteroids, and
  - No lesion >1.5 cm
- Individuals with previously treated CNS metastases may participate if:
  - Any prior CNS-directed therapy is completed, including radiation or surgery, ≥14 days prior to the first dose of study intervention
  - CNS disease is neurologically and radiologically stable, defined as without evidence of progression by repeat imaging for ≥14 days prior to the first dose of study intervention:
    - Individuals receiving glucocorticoid therapy must not receive >10 mg prednisone daily or equivalent
    - Individuals receiving prophylactic anticonvulsants must be on a stable dose for ≥14 days prior to the first dose of study intervention. Enzyme-inducing anti-epileptic drugs for CNS metastases must be discontinued for at least 5 half-lives prior to the first dose of study intervention
History of Grade 4 myelosuppression lasting >7 days, or Grade 3 myelosuppression requiring more than 6 weeks of recovery
Any unresolved toxicities from prior treatment greater than National Cancer Institute Common Terminology Criteria for Adverse Events (NCI-CTCAE) version 5.0 Grade 1 at the time of starting trial treatment except for alopecia and peripheral neuropathy
Prolongation of the corrected QT interval by Fridericia (QTcF) >470 msec during screening
- QTcF is calculated using Fridericia’s Formula: QTcF = QT/(RR^0.33)
- If QTcF >470 msec, perform 2 repeat ECGs and average the 3 results to assess eligibility
- Correction for underlying bundle branch block (BBB) is allowed
- If clinically safe to do so, and at the investigator’s discretion, correction of suspected drug-induced QTcF prolongation can be attempted with either discontinuation of the offending drug or changing to another drug that is not associated with QTcF prolongation
Significant cardiovascular disease, defined as having any of the following:
- Unstable angina within the past 2 months
- History of myocardial infarction within 6 months prior to planned start of trial treatment, or
- Grade ≥3 New York Heart Association functional classification system of heart failure, uncontrolled or symptomatic arrhythmias
Active uncontrolled systemic bacterial, viral, fungal, or parasitic infection (except for fungal nail infection), or other clinically significant active disease process that, in the opinion of the investigator and the sponsor, makes it undesirable for the individual to participate in the trial. Screening for chronic conditions is not required
Any concurrent severe or uncontrolled medical conditions that could increase the participant's risk for toxicity while in the study or that could confound discrimination between disease- and study treatment-related toxicities
Have a current infection with hepatitis B virus (HBV) that is positive for HBsAg and HBV DNA (detectable)
- Exception: Individuals with negative HBsAg and positive anti-HBc if HBV DNA is negative before C1D1
Have a current infection with hepatitis C virus (HCV) that is positive for HCV RNA. Screening for HCV is not required for individuals who do not have a history of HCV unless required by local regulations. Individuals previously treated for HCV are eligible for the study if they meet the following criteria:
- Completion of curative antiviral therapy
- HCV viral load below the limit of quantification 28 days of C1D1 or
- Negative hepatitis C antibody result OR, if positive, then must be hepatitis C RNA negative
Second primary malignancy, or an additional malignancy treated within 2 years of enrollment that is at high risk for progression or recurrence in the opinion of the treating investigator
- Exceptions:
  - Curatively resected non-melanomatous skin cancer
  - Clinically localized low risk prostate cancer on active surveillance
  - Curatively resected in situ cervical or breast cancers
Evidence of ongoing and untreated urinary tract obstruction; for example, hydronephrosis or hydroureter
Have received any therapy listed below within the specific window:
- Cytotoxic therapies or targeted agents that are small molecule inhibitors: ≤14 days or ≤5 half-lives, whichever is shorter
- Systemic anticancer therapy except for stable dose of hormone maintenance therapy if permitted by medical monitor: ≤14 days
- Antineoplastic monoclonal antibodies: ≤8 days
- Palliative limited field radiation: ≤7 days (or ≤14 days if CNS)
- Broad field radiation (≥30% of bone marrow or whole brain radiotherapy): ≤21 days
- Major surgery: ≤30 days
- Investigational therapeutic agents: ≤28 days or 5 half-lives (whichever is longer)
- Any therapeutic systemic radionuclides (eg, radium-223, rhenium186, strontium-89): ≤42 days
- Any therapeutic radioligands (eg, Lu-177 dotatate): ≤7 days or while on treatment
Previous hemi- or total-body radiation
Previous adoptive T-cell therapy (eg, CAR-T therapy, TCR therapy, etc)
Are currently enrolled, or were previously enrolled, in any other clinical study involving an investigational product or any other type of medical research judged not to be scientifically or medically compatible with this study
Known hypersensitivity to any component or excipient of planned LY4337713 therapy
Inability to lie flat during or tolerate SPECT, PET, CT, or MRI (MRI required only in participants with a contraindication to CT IV contrast)
Are pregnant, lactating, or intend to become pregnant during the study or within 31 weeks after last administration of LY4337713