Play was delayed by an hour and 12 minutes due to the threat of lightning at Hillside Golf Club but soft conditions and very little wind meant several players could threaten the course record of 63 recorded by Matthew Jordan in the opening round.
Starting on the back nine, Wallace made a steady start with birdies at the 11th hole and 17th.
The 29-year-old found the sand at the par-five fifth with his second shot but managed to get up and down to make it a three-way tie alongside Fisher and Lemke.
A brilliant approach set up a birdie from five feet for Wallace at the next hole as he grabbed the outright lead.
Lemke carded an incredible eight birdies in a row from the 13th to charge up the leaderboard with a 64, while Fisher signed for a 65.
Late starters Detry and Ramsay both finished with birdies on the final hole for rounds of 67 to remain in contention heading into the weekend.
Wallace has won four European Tour titles since 2017 and hopes to start challenging at major championships after surging to a career-high ranking of 35 earlier this year.
His quest to get to the top of the game has recently led him to hire fitness expert Steve McGregor, who has also worked with Rory McIlroy and Lee Westwood - two former world number ones.
"I've got a brilliant team with the inclusion of Steve now, his history speaks for itself getting two players to world number one," Wallace said.
"Two great players obviously, but if he can do some of that magic to me hopefully we can get to that position or close enough."
Overnight leader Jordan's progress was dampened by a double-bogey at the 11th but he recovered to post a 72, finishing three shots off the lead. Tournament host Tommy Fleetwood was a further two shots behind after a second-round 69.
(Reporting by Hardik Vyas in Bengaluru; Editing by Toby Davis)
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