Two strokes behind Stricker with three holes to play, Lehman closed with two birdies and a par for a 7-under 66 and a one-stroke victory over playing partner Stricker.
Stricker followed his second-round 63 with a 70. He was trying to become the 19th player to win in his first start on the 50-and-over tour and first since Miguel Angel Jimenez in 2014.
Stricker bogeyed the par-3 16th, matched Lehman with a birdie on the par-5 17th, and bogeyed the par-4 18th after hitting a 3-wood drive left into the water.
The 58-year-old Lehman won for the first time since the 2015 SAS Championship, finishing at 20-under 199 on Omni Tucson National's Catalina Course. He won the 1996 British Open and four other PGA Tour titles.
Lehman erased a three-stroke deficit on the first two holes, making a birdie and eagle, while Stricker opened with his first bogey of the week.
Bob Estes (67) tied for 23rd at 8 under in his senior debut.