Lawton was traded from the New York Mets to the Cleveland Indians during the winter of 2001. In the deal, the Mets sent Lawton, a players to be named later, Alex Escobar, and Jerrod Riggan to the Indians in exchange for Danny Peoples, Roberto Alomar, Mike Bacsik. The players to be named was Earl Snyder and Billy Traber, who were sent to the Indians two days later. On April 18, 2002, in a game against the Minnesota Twins, Lawton separated his right shoulder after diving for the ball in right field, but played through the injury. On May 18, Lawton hit a two-out, two-run home run in the bottom of the ninth inning to give the Indians a walk-off win against the Baltimore Orioles. On September 19, Lawton was placed on the disabled list, and was later forced to sit out the rest of the season after feeling pain in his labrum, which was torn earlier in the season. He played three rehab games in the minors that season with the Double-A Akron Aeros, getting no hits in 10 at-bats. There were rumors that Lawton may not be ready for the start of the 2003 season. On the season with the Indians, Lawton batted .236 with 71 runs scored 98 hits, 19 doubles, two triples, 15 home runs, 57 RBIs, and eight stolen bases in 114 games played. He played 85 games in right field, and 23 in left field. As an outfielder, he committed six errors, and made six assists and 229 putouts. He underwent arthroscopic surgery after the season to repair a tear in his labrum and fraying in the rotator cuff. Doctors also removed a cyst from his acromioclavicular joint.