Alexander was born on January 21, 1922, in a row house on Draper Street near Front Street and Spadina Avenue in Toronto, Ontario. He was the eldest son of Mae Rose (née Royale), who emigrated from Jamaica, and Lincoln MacCauley Alexander, Sr., a carpenter by trade who worked as a porter on the Canadian Pacific Railway, who had come to Canada from St. Vincent and the Grenadines. Lincoln had a younger brother Hughie, born in 1924, and an older half-brother Ridley "Bunny" Wright, born to his mother in 1920 prior to her marriage to his father. Bunny was never accepted by Lincoln Sr. and was not allowed in the family's house.