On July 31, 2001 the Minnesota Twins traded Lawton to the New York Mets in exchange for Rick Reed. During his time with the Mets, Lawton split time with outfielder Tsuyoshi Shinjo, Joe McEwing, Benny Agbayani, and Jay Payton. In his Mets debut on July 13, against the Houston Astros, Lawton got one hit in four at-bats. His first home run as a Mets player come on August 5, against the Arizona Diamondbacks. Lawton sometimes batted in the third position in the Mets' batting order. With New York that season, he batted .246 with 24 runs scored, 45 hits, 11 doubles, one triple, three home runs, 13 RBIs, and 10 stolen bases in 48 games played. Combined between the Twins and Mets that season, Lawton batted .277 with 95 runs scored, 155 hits, 36 doubles, one triple, 13 home runs, 64 RBIs, and 26 stolen bases in 151 games played. In his combined defensive stats as an outfielder, Lawton committed four errors; and made three assists, and 289 putouts.