The Italian, who made his Ryder Cup debut in Wales in 2010 but missed out two years later in Chicago, carded a four-under 68 on the East Course to join Lee (67) on 11-under 132 at the Royal Johannesburg and Kensington Club.
The competitors are playing two courses this week, the par-72 East and par-71 West.
Molinari has struggled with injury in the last couple of seasons but recent performances seem to suggest he is getting back to his best.
"I drove the ball really well," he told reporters. "I've been driving the ball like that for the last few months and it's making a big difference because I am hitting a couple of clubs less than I am used to and most times I am on the fairway.
"There are two rounds to go but I like the way I am hitting the ball. I made a few putts today but the most important thing is to keep hitting the ball like this."
A blistering best of the day 63 by David Horsey helped the Briton move into joint third place on 133 with South African George Coetzee (68) at the European Tour event.
Defending champion Richard Sterne of South Africa missed the cut after finishing on 141.
(Reporting by Mark Gleeson; editing by Tony Jimenez)
