This study is being done for the following reasons:

To determine the safety of LY2886721 and any side effects that may be associated with it and to see how much of the study drug is in the blood and the cerebrospinal fluid (CSF) when one dose is given to healthy participants and participants diagnosed with Alzheimer's disease. It will also look at how safe and tolerable the study drug is when given to healthy participants in higher doses.

This research study is being conducted in three groups, referred to as Groups (Cohorts) A, B, or C.

Group A will enroll participants with Alzheimer's disease while Groups B and C will enroll healthy participants.

For Group A or B, participation in this research study could last up to 34 days. For Group C, participation could last up to 60 days.

Inclusion Criteria:

• Healthy participants have a body mass index (BMI) of 19 to 32 kilograms per square meter (kg/m^2), inclusive, at screening. There are no restrictions on BMI in participants diagnosed with Alzheimer's disease.
• Healthy participants should not be taking any concomitant medications. For participants with Alzheimer's disease, concomitant medications will be determined by the investigator in consultation with the Lilly clinical pharmacologist on an individual basis.

Cohort A:

• Participants are defined as otherwise healthy males or females as determined by medical history and physical examination, and a diagnosis of Alzheimer's disease and must be at least 45 years of age.
• Meets National Institute of Neurological and Communicative Disorders and Stroke/Alzheimer's Disease and Related Disorders Association (NINCDS/ADRDA) criteria for probable Alzheimer's disease, as determined by a clinician approved by the sponsor or designee.
• Mini Mental State Examination (MMSE) score of 16 through 28 at screening.
• Modified Hachinski Ischemia Scale (MHIS) score of <4.
• Capable of understanding and signing their own informed consent, in the opinion of the investigator, or if the participant has a Legally Authorized Representative (LAR), then the LAR must be capable of understanding and signing the assent form, and the participant may or may not sign the informed consent, as to be determined by the investigator.
• If receiving concurrent treatment with an acetylcholinesterase inhibitor (AChEI) and/or memantine, the participant has been on a stable dose for at least 4 weeks before Day 1. Dosing must remain stable throughout the study. Note: If a participant has recently stopped ACHEIs and/or memantine, he or she must have discontinued treatment for at least 4 weeks before Day 1.

Exclusion Criteria:

• Have an abnormality in the 12-lead electrocardiogram (ECG).
• Have abnormal blood pressure.
• Have abnormal thyroid function as reflected by thyroid stimulating hormone (TSH) values outside of the normal range.
• Show evidence of human immunodeficiency virus (HIV) infection and/or positive HIV antibodies.
• Show evidence of hepatitis C and/or positive hepatitis C antibody.
• Have had multiple episodes of head trauma, or have a history within the last 5 years of a serious infectious disease affecting the brain.
• Have chronic hepatic disease.
• Have evidence or history of significant active bleeding or a coagulation disorder.
• Cohort A: have any neurological disorders other than Alzheimer's disease.
• For healthy participants (Cohorts B and C) only: Use or intend to use over the- counter or prescription medication, including herbal medications within 14 days prior to dosing or during the study.

All enrolled participants.