Argentine striker Lopez fired home from close range in the 90th minute as Lyon progressed from the group stage for the seventh time in a row.
Liverpool had gone ahead with a thunderbolt 25-metre shot from Ryan Babel in the 83rd.
Lyon top Group E with 10 points from four matches followed by Fiorentina (9), Liverpool (4) and Debrecen (0).
Rafa Benitez's side now need to win their last two matches and hope Fiorentina drop points.
Lyon coach Claude Puel praised Hugo Lloris for a superb performance in goal.
"He is the one who kept us in the game but that is no surprise," Puel told reporters. "He has played a prominent part in our Champions League results."
Fernando Torres, who has been suffering with a groin injury, started for Liverpool at Gerland stadium but the Spain striker was a shadow of his normal self.
He went close after 12 minutes when his effort was parried by France keeper Lloris but gradually faded out of the game.
Lloris also tipped a Dirk Kuyt lob over the bar before Andriy Voronin shot straight at the keeper when well placed.
BRILLIANT STOP
Liverpool continued to push forward in the second half, Lucas finding himself unmarked in the area only to be thwarted by a brilliant stop from Lloris.
With 15 minutes to go Lopez took advantage of a weak Sotiris Kyrgiakos header only to be denied by visiting keeper Pepe Reina.
Liverpool went in front thanks to Babel's stunning right-foot drive before Lyon snatched the draw they needed to advance when Kyrgiakos missed the ball in the box, leaving Lopez unmarked to beat Reina from close range.
"You have to be really disappointed because it was a great opportunity tonight," said Benitez. "We had our chances, again a late goal against Lyon (makes) a massive difference.
"It is difficult but not impossible. We have to win our next game (at Debrecen on November 24) and see what happens between Fiorentina and Lyon the same night. We have done it in the past.
