Tennessee (24-3, 12-0 SEC) has won 15 straight since losing to Connecticut in overtime Jan. 4. LSU (23-2, 10-2) had won eight straight and 17 consecutive home games before Sunday.
Lawson finished with 12 points, including nine in the last five minutes. Gwen Jackson and Shyra Ely each scored 12 points for Tennessee.
Temeka Johnson led LSU with 18 points, Aiysha Smith had 15, Doneeka Hodges scored 14 and Seimone Augustus added 12.
LSU opened the second half with a 14-8 run to go up 46-38 with 14:44 remaining. Tennessee came back, pulling to 49-48 on a layup by Shyra Ely with 10:29 to go.
LSU stretched the lead to four points on back-to-back baskets by Johnson to go up 52-48. The Vols took their first lead of the second half on a layup by Lawson to make it 59-58 Tennessee with 4:03 left.
Tennessee went up 62-60 on a 3-pointer by Lawson, the Volunteers' only 3-pointer of the game. LSU answered with a 3-point basket by Johnson to go ahead 63-62 with 2:05 left, the Tigers' final lead.
Lawson hit a jumper at 1:40 to make it 64-63 Tennessee, then added two free throws, increasing the lead to 66-63 with 24 seconds left. A layup by Johnson pulled LSU to 66-65.
LSU fouled Shanna Zolman, who made both shots, giving Tennessee a 68-65 lead. The Tigers got the ball for the final time with two seconds left, but Lawson stole it to seal Tennessee's victory.