The players shared first-team snaps with the offense Monday.
Livings, who started all 16 games last season, suffered a foot injury before training camp, allowing Leary to get snaps with the first-team offense.
"I'm cool with it," Leary said regarding the rotation. "I do what the coaches tell me to do. If that's what they tell me to do, that's what I do."
When asked whether he is rusty, Livings said, "It's my fifth practice, so I'm just getting back in it."
Leary started training camp practices on time but suffered a calf injury early in training camp and made his return to the practice fields Monday.
"I know I’m going to be a little winded because there’s nothing like football shape," Leary said after the Monday morning walk-through, "but just getting my feet up under me, and get my hands right and get those physical reps."
The Cowboys are not immune to using rotations along the offensive line.
Doug Free and Jermey Parnell rotated snaps at right tackle in the last month of the 2012 regular season. There was a thought Parnell would compete with Free for the starting job this season, but he suffered a hamstring injury, possibly ending any competition between the players.