For much of his career, he was used as a left-handed specialist. This type of pitcher is used against an opposing team's star left-handed hitter(s) late in a game. Lloyd excelled in this role for the New York Yankees in 1998 when he posted a career-best 1.67 ERA. This effectiveness led to the Toronto Blue Jays demanding Lloyd be included in a package anchored by starting pitcher David Wells when the Yankees traded for Toronto starting pitcher Roger Clemens.
Lloyd became a two time World Series champion for the Yankees in 1998, defeating the San Diego Padres. Lloyd is still the only Australian-born baseball player to have won a World Series.