Guy Boros and Steve Runge each fired 9-under-par rounds of 63. They are tied for third place with Todd Demsey (66), Omar Uresti (66) and Bo Van Pelt (67) at 13-under-par 131.
Lile got his amazing round going with a birdie at the par-5 second. After parring the third, he ran off three consecutive birdies from the fourth.
The South African capped his front nine with back-to-back birdies starting at the eighth. Around the turn, he notched his third consecutive birdie at the 10th for his seventh birdie of the day.
Lile cooled off with a pair of pars starting at 11, but got back on the birdie train at the par-4 13th. Starting at the par-4 15th, Lile began his final outstanding stretch of golf.
He birdied the 15th and followed with another at the next. Lile made it three straight at the 17th to give him a slim chance for a 59.
Lile needed to hole out for eagle at the par-4 18th for 59. He flirted with history but his second shot came to rest just over two feet from the cup. He tapped in for his 12th birdie of the day.
'I had some blood flowing on that second shot on the last hole,' said Lile. 'That is the longest two-and-a-half-foot putt I've ever had in my life. I don't think I've ever read a scorecard with as many 2s and 3s. Things were just going my way. Even when I was trying to two-putt they were going in.'
Lile needed just 24 putts for a round which saw him post 6-under 30s on both the front and back nines.
'That was the most ridiculous five hours I've ever spent in my life,' said Lile with a laugh. 'I went out thinking I needed a good round to make the cut. I think I'll make the cut.'
Rose, meanwhile, did not exactly struggle during his round. After opening with three pars, he reeled of five successive birdies from the fourth to climb to 11-under for the tournament.
He did drop a shot at the 12th, but rebounded with back-to-back birdies from the 13th and again from the 16th to grab a share of the lead.
'I'm definitely pleased with the round,' said Rose, who carried a hot putter himself. 'It is out there if you can keep yourself going. You just can't let up out here. A lot of putts were going in for me today. I got a tip from Jeff Freeman earlier in the week because I had been struggling with the putter.'
Scott Petersen fired a 7-under 65 Friday to move to 12-under-par 132. He shares eighth place with Scott Gutschewski, who posted a second-round 67. Steve Ford, Bob Heintz and Ted Purdy are one stroke further back at minus-11.
The cut line fell at 5-under-par 139 with 73 players advancing to the weekend. Jay Delsing, the defending champion, survived the cut by one stroke. He stands at 6-under-par 138 after a 2-under 70 on Friday.