YORKSHIRE set Hampshire 298 to win from a minimum of 72 overs before rain forced an early lunch at the Ageas Bowl.
The visitors scored 95 runs in 22 overs on the fourth and final morning to take their second innings score to 238-5.
But no sooner had the champions declared 25 minutes before lunch than rain began to fall.
Yorkshire are seeking a victory that would likely send them top of the table, with Middlesex having so far been unable to get on the field at Edgbaston today, where Warwickshire are 74-3 chasing 338.
Yorkshire started the day on 143-2, with Gary Ballance on 46 and Andrew Gale on 19.
Gale fell to the eighth ball of the day without adding to his score, caught behind off Brad Wheal.
Lehmann found Wheal’s bowling to his liking as he twice dispatched him to the offside boundary.
After a circumspect start, Ballance also found his rhythm after bringing up his half-century from 86 balls with 10 fours.
The England left-hander had advanced to 72 when he was fourth out with the total on 189, bowled by Berg to give the former Middlesex man his 200th wicket in first-class cricket.
Tim Bresnan thumped 27 from 34 balls with five fours before miscuing an attempted pull off Andy Carter to mid-off, where Berg took a fine catch diving forward.
Yorkshire pulled out six balls later, with Lehmann unbeaten on 35 and Andy Hodd on one.