The visitors made the breakthrough as early as the first minute when Chahir Belghazouani fired in from outside the penalty box into the top-left corner of the Lorient goal.
However, Ajaccio restored their two-goal advantage five minutes from time through an Eduardo long-range effort.
Eduardo made it 4-1 on the stroke of half-time with a fierce shot from outside the hosts' 18-yard box.
Lorient refused to give in though and found the target for the second time in the afternoon just a minute into the second half.
Then 11 minutes from time Aliadiere scored his second goal of the match when he turned home Ludovic Giuly's headed pass from close range.
Giuly himself came close to equalising for Lorient seven minutes from time but failed to keep his shot on target.
However, the hosts rescued a point in dramatic fashion, as Gilles Sunu turned in Traore's cross from close range in the fourth minute of injury time.