Madrid sunk by Makoun missile
Lyon picked up a third successive home win over Real in the Champions League after the Cameroon midfielder drove a stunning 25-metre shot into the top corner of the net in the 47th minute.
Real, who last reached the quarter-finals in 2004, dominated possession but failed to create many chances despite Cristiano Ronaldo's efforts up front.
The Madrid club, hoping to reach the final in May at their own Bernabeu stadium, host Lyon in the second leg on March 10.
"Lyon were physically very strong, they ran a lot and prevented us from playing our game. We weren't able to find the solutions," Madrid coach Manuel Pellegrini told reporters.
"This is a bad result for us as we conceded a goal and weren't able to score one. We'll have to put our game in order in the second leg but I have confidence in my players and I am sure we are able to do it," he added.
Lyon coach Claude Puel said his players could not be complacent despite having a slight advantage.
"We played a really good game tonight against a good team and we managed to play at a higher level both individually and collectively," he told reporters.
"I just slightly regret that we did not score a second goal after the break. The most important part of the job is still to come. There is a second leg and the only positive result is to qualify," he added.
Nine-times European champions Real took control in the first half without seriously threatening home goalkeeper Hugo Lloris.
Ronaldo tried to set up Gonzalo Higuain in the box with a clever back-heel but Lyon's defenders reacted more quickly than the Argentine striker.
Sidney Govou went close for Lyon with two early volleys and the hosts almost broke the deadlock before the interval when a superb long-range volley by Cesar Delgado hit the post.
Makoun put the home team in front soon after the restart and Lisandro Lopez almost made it 2-0 when he shot just wide.
Lloris then saved a deflected shot by Ronaldo and another attempt by Higuain from close range to keep a clean sheet.