Drafted 2nd overall by the Toronto Blue Jays in the 1978 amateur draft, Lloyd made his major league debut on May 24, 1980. Despite some growing pains early in his career, Moseby developed into a well-polished batter, fielder and base-runner, knocking in nearly 100 runs on several occasions and regularly stealing 30-plus bases.
In the mid-80s he was part of a powerful outfield trio for the Jays, playing center field between George Bell and Jesse Barfield. After the 1989 season, Moseby signed with the Detroit Tigers. Moseby saw limited time with the Tigers for two seasons, and then traveled to Japan, where he played with the Yomiuri Giants for 1992 and 1993.
Over his career, Moseby had 869 runs, 169 HRs, 737 RBIs, 280 SBs while batting .257. He was an All-Star in 1986.
Most recently, Moseby served as the Blue Jays' first base coach in 1998 and 1999.