Lyon struggled to create chances until centre back Lovren put them in front when he headed home Clement Grenier's corner kick in the 25th minute.
The seven-times French champions tightened their grip on the match but Bafetimbi Gomis twice shot narrowly wide.
Ajaccio goalkeeper Guillermo Ochoa made a couple of great saves after the break, parrying Grenier's fine lob and stopping a point-blank Gomis header.
Boosted by Romanian striker Adrian Mutu, who came off the bench to make his Ligue 1 debut, Ajaccio pushed hard to level, only for Lopez to double the advantage after a lightning counter-attack on 75 minutes.
"We knew it would be difficult. We tried to do our best but unfortunately, we did not get a point," Mutu told French channel Canal Plus.
"I am very confident I'll soon be in better shape."
In Rennes, Traore put the visitors ahead in the 23rd minute with a stunning shot from 30 metres and doubled his side's lead with a free kick from the same distance minutes before halftime.
Lorient, who had defender Maxime Baca sent off after 32 minutes for a rough challenge on Jonathan Pitroipa, were reduced to nine early in the second half when goalkeeper Fabien Audard was shown a red card for fouling Pitroipa.
Pitroipa pegged one back for the hosts who had Cheick Diarra sent off for a dangerous tackle on Traore with 11 minutes left.
Lorient are third on 11 points from five games and Rennes, who suffered their fourth defeat, are 18th.