Forward Kevin Gameiro exploited a blunder from Croatia defender Dejan Lovren to volley home from close range on four minutes and send Lorient into the last four.
In the semi-finals, the Brittany side will meet holders Girondins Bordeaux or second division Sedan, facing each other in the quarter-finals next week.
Lyon, who were knocked out of the French Cup in the round of 32 by Monaco on Sunday, lie fifth in the Ligue 1 standings, 11 points off leaders Girondins Bordeaux, and will face Real Madrid in the first knockout round of the Champions League.
All that means the seven-times Ligue 1 champions, who were the measure of all things in France for years, face the prospect of ending the season without a title.
Olympique Marseille needed a goal by midfielder Mathieu Valbuena nine minutes from time to beat 10-man Lille 2-1 in later League Cup action.
Visitors Lille opened the scoring through Brazilian forward Tulio de Melo on four minutes but Marseille responded through Argentine playmaker Lucho Gonzalez five minutes later.
The turning point came shortly before the hour when Lille had midfielder Yohan Cabaye sent off for a second booking.
Marseille then stepped up a gear and Valbuena sent them through to the last four with the winner from the edge of the box.
Marseille will next face Toulouse, who reached the semi-finals with a 1-0 win at second division Guingamp, the French Cup holders, courtesy of a second-half goal from defender Albin Ebondo.
In French Cup round of 32 action, third division Plabennec, who knocked out Nice in the previous round, scored another upset by winning 2-0 at Nancy with second-half goals from forward Vincent Crehin.
