Lukwiya, an ethnic Acholi, grew up in the town of Kitgum. His father, a fishmonger, drowned when Lukwiya was 12. His mother was a petty trader who smuggled tea across the border with Sudan to trade for soap. Lukwiya was one of four sons. While his mother started teaching him how to smuggle goods by bicycle, Lukwiya began to prove himself to be an extraordinary student. He came in at the top of his class in grade school, received the top school-leaving marks in the country, going on to attend university and medical school through a series of scholarships. He took a position as a medical intern at St. Mary's, a Catholic missionary hospital, in 1983.