The American was facing his third shot to the par-five eighth hole at Bellerive Country Club when an approaching thunderstorm forced play to be suspended on Friday afternoon.
Australia's Adam Scott and Jason Day clawed their way back into contention before play was suspended midway through the second round at the US PGA Championship.
That put him at 10-under 130, breaking by one the PGA Championship record and tying the 36-hole score for all majors.
Kisner, Koepka and South African Charl Schwartzel each flirted with the lowest all-time major round of 62 fired by South Africa's Branden Grace in the third round of last year's British Open at Royal Birkdale.
Open Championship runner-up Kisner holed six birdies as he played his first nine holes in 29 shots to move into the lead on nine under, while Woodland avenged a bogey on the 14th with an eagle three on the par-five 17th. Tiger Woods birdied three of his first five holes played.
After two more solid shots at the par-4 ninth, Day will face a 22-foot birdie putt when play resumes.
"I knew the golf course would be very playable this morning so I thought if I came out and shot two under it would be a very good score", said Lowry, speaking to RTE Sport after he completed his second round.
The third round was due to begin about 30 minutes after the end of the second round on Saturday, with players going out in groups of three - instead of the traditional two - off the first and 10th tees. "I think we'll see some putts go in".
"I feel safe because I feel safe where my game is", Woodland said.
"It's always a bit frustrating to have to come back and finish a round in the morning, but that's golf, and something I will just have to deal with", Fox said after his truncated round. The golf course is gettable and I'm holing a few putts.
"I'm all right with it", Kisner said. "We're going to have a pretty good battle if I can keep up with him".
"For me, I'm very happy with where I'm at". "Hopefully I can go shoot a low one this afternoon". "I didn't know that was such a rivalry". "I hit it well on the second nine". I have more people coming in this weekend.