Lehman ended the European Senior Tour finale at 12-under-par 204. It was Lehman's first win on that tour.
The 1996 British Open champion managed eight pars and a single bogey on the front nine at Constance Belle Mare Plage.
Around the turn, Lehman got back to even-par for his round with a birdie on the par-five 13th. He then birdied the 16th for the first time all week before making par on the final two holes to fend off Frost.
The South African Frost closed with a two-under 70 to end at minus-11. After two bogeys and two birdies on the front nine, Frost birdied the 13th and 14th to get to 11-under.
That moved Frost into a share of the lead with Lehman, but Frost fell one back with a bogey on 15. After Lehman birdied 16 to go two clear, Frost got back within one with a birdie at 17. Like Lehman, Frost only managed a par on the par-five 18th to finish one back.
Nick Job (71) took third at five-under-par 211, while Sam Torrance (66) and Gordon J. Brand (66) shared fourth at minus-four.
Peter Fowler closed with a 73, but his seventh place finish was enough to give him the John Jacobs Trophy for topping the Senior Tour Order of Merit. He finished more than 31,000 euros ahead Barry Lane, who tied for ninth after a final-round 73 of his own.