A Study of LY2599666 in Healthy Participants and Participants With Mild Cognitive Impairment or Alzheimer's Disease (AD)

Inclusion Criteria: Healthy Participants Part A: * Overtly healthy males or females as determined by medical history and physical examination * Have a body mass index (BMI) between 18.0 and 32.0 kilograms per meter squared (kg/m²), inclusive Participants With Mild Cognitive Impairment or Alzheimer's Disease (AD) \[Part B and C\]: * Participants are at least 50 years old at screening * Present with Mild Cognitive Impairment (MCI) due to Alzheimer's Disease (AD) or mild-to-moderate AD * Have a caregiver/study informant who provides a separate written informed consent to participate * Have adequate vision and hearing for neuropsychological testing in the opinion of the investigator * Positive florbetapir scan Exclusion Criteria: All Participants * Are currently enrolled in a clinical trial involving an investigational product or off-label use of a drug or device or are concurrently enrolled in any other type of medical research judged not to be scientifically or medically compatible with this study * Have known allergies to LY2599666, solanezumab, or any related compounds or components of the formulations, or have a history of significant atopy * Have an abnormality in the 12-lead electrocardiogram (ECG) that, in the opinion of the investigator, increases the risks associated with participating in the study * Have an abnormal blood pressure as determined by the investigator * Have significant allergies to humanized monoclonal antibodies, diphenhydramine, epinephrine, or methylprednisone * Require treatment with other monoclonal antibodies Participants With Mild Cognitive Impairment or Alzheimer's Disease (AD) \[Part B and C\] * Have medical or surgical conditions in which lumbar puncture and or/catheter insertion is contraindicated * Have any contraindication for magnetic resonance imaging (MRI) studies, including claustrophobia, the presence of metal (ferromagnetic) implants, or a cardiac pacemaker that is not compatible with MRI Participants With Mild Cognitive Impairment or Alzheimer's Disease (AD) \[Part C\] * Have had lymphoma, leukemia, or any malignancy within the past 5 years except for basal cell or squamous epithelial carcinomas of the skin that have been resected with no evidence of metastatic disease for 3 years, cervical carcinoma in situ, or in situ prostate cancer with a normal prostate-specific antigen post treatment