Lehmann, appointed captain while Travis Head is on Australian duties, struck 115 of SA's 307 all out in Adelaide, with Ben Manenti making 71.
Tasmania are 1-94 at stumps with Caleb Jewell on 45 and Charlie Wakim 36.
The South Australians were in morning trouble at Karen Rolton Oval on Tuesday after losing 4-19 in a horror nine-over stretch.
Openers Kelvin Smith (21) and Henry Hunt (16) put on 30 runs at a healthy clip before the tumble.
Smith was superbly caught, high to his left, by first-class debutant Mitchell Owen at third slip.
Paceman Gabe Bell doubled up by dismissing Daniel Drew (six), nicking to first slip, before Owen captured his maiden Shield wicket.
Hunt feathered a glove to a leg-side short ball and the 22-year-old medium-pacer Owen, in his next over, bowled Nathan McSweeney (two), the Redback chopping on attempting an off-side leave.
At 4-49, Lehmann and recruit Jake Fraser-McGurk, the promising 21-year-old who departed Victoria in the off-season, launched a daring counter-attack.
The pair smacked 59 runs from seven overs - Fraser-McGurk's 37 from 23 balls featured two sixes and five fours before skying to mid-on from spinner Jarrod Freeman before lunch.
Lehmann posted his half-century during a brisk seventh-wicket stand with the aggressive Manenti, who followed suit in reaching his milestone from 45 balls.
The pair put on 104 runs for the seventh wicket with Manenti's rapid-fire 60-ball knock including 11 fours and two sixes.
Lehmann, with valuable tail-end support from Wes Agar (23) and Brendan Doggett (12), continued to his 10th first-class ton - his 143-ball gem included 18 fours.
Tasmanian quick Bell (3-68), Owen (2-42), Freeman (2-36) and Lawrence Neil-Smith (2-82) were multiple wicket-takers.
8°C