Lee carded a four-under-par 66, the joint lowest round of the day, to set the clubhouse target on nine under par and looked on as none of the later starters were able to overhaul him at Pretoria Country Club.
Horsey held the outright lead after three birdies and one bogey in his first 12 holes, but bogeyed the 17th to card a second consecutive 69, while overnight leader Adrian Otaegui struggled to a 72.
There are 15 players within three shots of the lead, setting up the potential for a thrilling finish on Sunday.
Last week’s Africa Open winner Trevor Fisher Jnr recovered from four bogeys in his first seven holes to post a 69 and was joined in the lead by fellow South Africans Wallie Coetsee and George Coetzee, who is a member of the club and won his first junior competition there aged 10.
Otaegui, who is a protege of former Masters champion and 2012 Ryder Cup captain Jose Maria Olazabal, was two shots clear after a second round of 62 but dropped his first shot on the front nine all week when he bogeyed the third.
The 22-year-old responded with birdies from close range on the sixth and eighth and looked in position to pick up another shot on the par-five ninth when his second shot bounded through the green, only to duff two chips and eventually card a bogey six.
Further bogeys followed on the 10th and 13th and although he birdied the 15th, Otaegui also dropped a shot on the 16th after his tee shot flew over the green.