Lawrence won the job in fall drills but missed three games early in the season with a broken fibula. He had 106 yards on 18 carries in last week's victory over Texas and is third on the team with 301 yards, a 4.2-yard average and three touchdowns.
Moore has battled injuries and has only 39 yards with a 2.6-yard average.
Center Travis Ruth is probable this week against Texas Tech after missing the Texas game with an undisclosed injury. Cornerback Kip Edwards (foot) might be a game-time decision and kicker Grant Ressel will be miss his fourth straight game.