Lawson scored 16 points in the second half, including seven when the Tigers finally broke open the game with a 15-2 run that gave Memphis its first double-digit lead and left it ahead 73-57 with 2:38 to go.
Lawson finished 12 of 18 from the field and the freshman forward picked up his third double-double.
The Redhawks (0-7) trailed by only two at halftime before absorbing its 10th straight road loss dating to last season. Marcus Wallace led Southeast Missouri with 16 points.
The Tigers outscored the Redhawks 54-30 in the paint. Neither team shot well from the arc with the Tigers 3 of 16 and the Redhawks 3 of 12.