Lawton began the 1995 season in the minor leagues with the Hardware City Rock Cats of the Double-A Eastern League. With the Rock Cats, he batted .269 with 75 runs, 111 hits, 19 doubles, five triples, 13 home runs, 54 RBIs, 26 stolen bases, and 56 walks in 114 game played. The Minnesota Twins called Lawton up in September of that year. He made his debut in Major League Baseball (MLB) on September 5, against the Detroit Tigers. In that game, Lawton struck out in one at-bat. Lawton got his first hit of his major league career on September 6, against the Tigers. On September 28, against the Cleveland Indians, Lawton hit his first career major league home run. In the majors that year, Lawton batted .317 with 11 runs scored, 19 hits, four doubles, one triple, one home run, and 12 RBIs in 21 games played. On defense with the Twins, Lawton played 12 games in center field, eight games in right field, and one game in left field. After the 1995 season, Lawton played in the Arizona Fall League.