Lovemark followed an opening-round 68 with a 69 on Friday to climb into a tie with List at 3-under for the tournament.
Alongside McIlroy, two-time Honda Classic victor Pádraig Harrington finished well outside the cut mark after a second consecutive 76 for a total of 12 over while Seamus Power was only one shot better off after a 74.
With the 36-hole cut now projected to fall at four-over, Scott could suffer his third missed cut in his past four worldwide starts when play is finished on Friday.
"Only one bogey", List told reporters.
"I just missed the rush of competing for a Green Jacket", he said on Wednesday of his injury-enforced absences. Berger held the lead at 5-under with consecutive birdies at Nos. He's effectively hit delicate chip shots and demanding bunker shots. But heading into the Honda Classic, Woods said he was once again getting used to the cadence of playing professional golf and acclimating to the ramped-up pressure when a scorecard is in his pocket.
He was level par for his round after 14 holes with three birdies and three bogies on his card.
Thomas' scorecard included 17 pars.
"I felt comfortable out there today", Woods said. "To have 3-under leading after two rounds - that's often the cut (line) out here".
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Woods was able to finish strong, though, by chipping to inches for a birdie at the par-5 18th - his first birdie on a par 5 all week.
"I'm very pleased", said the 14-time Major champion, who had three birdies, a bogey and a double bogey in hard, blustery conditions at PGA National in Palm Beach Gardens, Florida.
Woods missed, but with the leaders falling back to him on this grueling day, he stuck his approach at the 12 to 10 feet to give himself a chance to move within a shot of the lead.
However, the 42-year-old former world number one birdied the 17th and closed with a par to sit in a tie for 14th in his third tournament of 2018 as he continues his latest comeback following back surgery last year. "Overall, it was a grind out there and it's tough to make putts in the wind". It was tough.it's tough to make putts out there. "I did that for most of the day".
After starting from the tenth, Lahiri was two-under through 13 holes before he dropped the bogeys on fifth, seventh and eighth. Simpson is now part of a group one shot back at minus-two with Russell Henley, Rory Sabbatini and Tommy Fleetwood.
"It's very relentless", List said.
"It's going to come down to a pretty bunched leaderboard on Sunday and we all know that".
NOTES: Danny Lee withdrew on Thursday due to undisclosed personal reasons.
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