Serbian third seed Djokovic, who has reached the semi-finals here just once before, beat Lu 6-3, 6-2, 6-2 on Court One to book his spot in the last four.
Djokovic faces Berdych in the semi-finals.
Spanish world number one Nadal, the 2008 winner who missed the chance to defend his title last year due to knee injuries which are still plaguing him, takes on Swedish sixth seed Robin Soderling, in a re-run of this year’s French Open final earlier this month.
British home favourite Murray faces French 10th seed Jo-Wilfried Tsonga in the other quarter-final.
Berdych, the first Czech man to reach the Wimbledon semi-finals since Ivan Lendl in 1990, said he could hardly believe he had put out the world number two on his stomping ground.
“It’s amazing to play in this stadium, to play such a great player as Roger is and come here and be a winner, this is really amazing for me,” he said. “If I go through my career, I think it was so far the toughest game to serve and close out the match.”
On Court One, Lu had put out three-times beaten finalist Andy Roddick to get through to the last eight — the best-ever Grand Slam performance by a Taiwanese player — but was no match for the in-form Djokovic.
“The way I have played I think I deserve to win.
“I was hitting all the shots and I was really playing very solid from all parts of the court so I’m very, very happy with the performance,” the Serb said.
“I sincerely hope to continue with this level of my game. The way I have been playing match after match is very encouraging. I’ve nothing really to lose in the semifinals.”