The study involves repeated doses of LY3303560 given by infusion for 49 weeks. The study will examine how safe repeated doses of LY3303560 are, whether they cause side effects in participants with mild cognitive impairment or Alzheimer's Disease, and how LY3303560 is handled by the body and acts in the body. This study will last up to 65 weeks, not including screening. Screening is required within 90 days prior to the start of the study.

Inclusion Criteria:

• Mild Cognitive Impairment (MCI) due to Alzheimer's Disease (AD) or mild-to-moderate AD based on National Institute of Aging and Alzheimer's Association diagnostic criteria

• Female participants: women not of child-bearing potential may participate, and include those who are:

  • Infertile due to surgical sterilisation (hysterectomy, bilateral oophorectomy, or for countries outside of Japan, tubal ligation), congenital anomaly such as mullerian agenesis; or
  • Postmenopausal defined as women at least 50 years of age with an intact uterus who have not taken hormones or oral contraceptives within 1 year, who have had either cessation of menses for at least 1 year, or 6 to 12 months of spontaneous amenorrhea with follicle-stimulating greater than (>) 40 milli-international units per millilitre (mIU/mL)

• Have a body weight of at least 50 kilogram (kg) (except for Japanese sites) and have a body mass index (BMI) of 18.0 to 35.0 kilogram per meter square (kg/m²) (for all sites), inclusive, at screening

Exclusion Criteria:

• Are currently enrolled in a clinical trial involving an investigational product (IP) or any other type of medical research judged not to be scientifically or medically compatible with this study
• Have participated, within the last 30 days (3 months and 4 months for sites in the European Union [EU] and Japan, respectively) in a clinical trial involving an IP. If the previous IP has a long half-life, 3 months (4 months for sites in Japan) or 5 half-lives (whichever is longer) should have passed
• Have known allergies to LY3303560, related compounds or any components of the formulation, or history of significant atopy
• Have significant allergies to humanised monoclonal antibodies, diphenhydramine, adrenaline, or methylprednisolone; or have a history of clinically significant multiple or severe drug allergies, or intolerance to topical corticosteroids, or severe post treatment hypersensitivity reactions (including, but not limited to, erythema multiforme major, linear immunoglobulin A dermatosis, toxic epidermal necrolysis, or exfoliative dermatitis)
• Have an increased risk of seizures as evidenced by a history of head trauma with loss of consciousness within the last 5 years or any seizure; prior electroencephalogram with epileptiform activity; surgery to the cerebral cortex; or history within the last 5 years of a serious infectious disease affecting the brain
• Have any contraindications for Magnetic Resonance Imaging (MRI) studies, including claustrophobia, or the presence of metal (ferromagnetic) implants or a cardiac pacemaker
• Have a history of intracranial haemorrhage, cerebrovascular aneurysm, or arteriovenous malformation, carotid artery occlusion, or epilepsy
• Have received acetylcholinesterase inhibitors (AChEIs), memantine, and/or other AD therapy for less than 4 weeks, or have less than 4 weeks of stable therapy on these treatments by time of randomisation (including less than 4 weeks since stopping AChEIs and/or memantine); or have received medications that affect the central nervous system, except treatments for AD, for less than 4 weeks at a stable dose
• Have used stable medical therapy for less than 2 months by time of randomization for any concurrent medical condition that is not exclusionary
• Are currently using or intend to use drugs known to significantly prolong the QT interval, or who have a known risk factor for Torsades de Pointes. A participant will not be excluded if they have been using stable medication that is known to potentially cause significant prolongation of the QT interval, but does not present with any clinically significant prolongation of the QT interval at screening, in the opinion of the investigator
• History of cancer within the last 5 years, with the exception of non-metastatic basal and/or squamous cell carcinoma of the skin, in situ cervical cancer, non-progressive prostate cancer, or other cancers with low risk of recurrence or spread.