The right-handed Dolgopolov, No. 38 in the world, had to take an injury timeout in the fifth game of the second set after hitting his left thumb with the frame of his racket on a forehand shot.
"I couldn't feel it much for a few games," Dolgopolov said.
"It just aches — not a hard pain, but it threw off my concentration a bit.
"Stuff like that happens.
"You have to deal with it and get back as fast as you can."
Dolgopolov, who had a half-inch cut on the first knuckle of his left thumb, lost serve in that game.
But he broke right back in the sixth game, then registered another service break two games later.
"I wasn't happy I lost the break," said Dolgopolov, who had nine aces against the 62nd-ranked Lu.
"I was serving pretty solid all match, but after that, I gave away three points that he didn't do much to break.
"After that, I did pretty well for a few games."
Dolgopolov advanced to a tournament semi-final for the first time this season, and will play either Spain's Fernando Verdasco or France's Gael Monfils Friday at the Wake Forest Tennis Centre.
In other quarter-final matches scheduled Thursday, Russian Dmitry Tursunov faces Austria's Jurgen Melzer in an afternoon match, and American Sam Querrey — at No. 29, the highest ranked player remaining in the field — will play Ricardas Berankis of Lithuania.
Results on Thursday in the ATP Winston-Salem Open:
Alexandr Dolgopolov (UKR x10) bt Lu Yen-Hsun (TPE) 7-6 (7/2), 6-3