A Study of LY3451838 in Participants With Migraine

Inclusion Criteria: * Must have a diagnosis of migraine with a history of migraine headaches of at least 1 year prior, and migraine onset prior to age 50. * Have completed at least 80% of required daily diary entries during the start of the study. * Have documentation of previous failure of 2 to 4 standard-of-care migraine preventive medication categories in the past 10 years. * Women of child-bearing potential must test negative for pregnancy as indicated by a negative serum pregnancy test and negative urine pregnancy test. * Women of child-bearing potential who are abstinent or in a same sex relationship must agree to either remain abstinent or to avoid sexual relationships with males. * Women of child-bearing potential who are not abstinent, must agree to use one highly effective method of contraception, or a combination of two effective methods of contraception during the study, as well as 5 months following. * Women not of childbearing potential may participate and include those who are: A. Infertile due to surgical sterilization (hysterectomy, bilateral oophorectomy or tubal ligation) or congenital anomaly; or B. Post-menopausal - defined as either: * i. a woman at least 40 years of age with an intact uterus, not on hormone therapy, who has cessation of menses for at least 1 year without an alternative medical cause, and a follicle-stimulating hormone greater than (\>) 40 multi-international units per milliliter (mIU/mL); or * ii. a woman 55 or older not on hormone therapy, who has had at least 12 months of spontaneous amenorrhea; or * iii. a woman at least 55 years of age with a diagnosis of menopause prior to starting hormone replacement therapy Exclusion Criteria: * Are currently enrolled in any other clinical study or any other type of medical research judged not to be compatible with this study. * Have participated, within the last 30 days or 5-half-lives (whichever is longer), in a clinical study involving any investigational product. If the half-life of the investigational product is unknown, 6 months should have passed prior. * Known hypersensitivity or intolerance to monoclonal antibodies or other therapeutic proteins, or to common antihistamines, epinephrine, methyl prednisone or other systemic corticosteroids. * Are currently receiving medication or other treatment for prevention of migraine headaches. Participants must have discontinued such medications or treatments at least 2 weeks prior. Botulinum toxin A or B that has been administered in the head or neck area use must be discontinued at least 3 months prior. Nerve blocks or device use (such as transcranial magnetic stimulation or electrical nerve stimulation) in the head or neck area for migraine treatment must be discontinued at least 30 days prior. Anti-calcitonin gene-related peptide (CGRP) antibodies must be discontinued at least 5 half-lives prior. * Have previously failed more than 4 migraine preventive medication categories in the past 10 years due to inadequate efficacy (that is, maximum tolerated dose for at least 2 months) and/or safety / tolerability reasons. * History of cluster headache or migraine subtypes including hemiplegic (sporadic or familial) migraine, ophthalmoplegic migraine, retinal migraine, typical aura without headache, complications of migraine and migraine with brainstem aura (basilar-type migraine). * In the 3 months prior, have other types of headache besides migraine, tension type headache, or medication overuse headache (MOH). (In other words, participants can have migraine, tension type headache, or MOH in the 3 months prior, but they cannot have other types of headache in that time). * History of head or neck injury within last 6 months. * History of traumatic cervical or head injury associated with significant change in the quality or frequency of headaches. * Have reading of electrocardiogram (ECG) showing abnormalities considered incompatible with the study. * Any liver tests outside the normal range. * Evidence of significant active or unstable psychiatric disease. * Women who are pregnant or nursing. * Participants who have used opioids or barbiturate-containing analgesic \>4 days per month for the treatment of pain in each of the past 3 months. * History of drug or alcohol abuse/dependence within 1 year. * Have a positive urine drug screen for illicit drugs. * Are unwilling or unable to comply with the use of data collection devices.