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 hormon…