Osimhen was in action for 58 minutes but could not continue his goalscoring run at Stade Pierre-Mauroy having previously scored all seven league goals in his last five home games.
Goals from Benjamin Andre, Yusuf Yazici and second-half substitute Loic Remy helped Christophe Galtier's side to a comfortable win on Saturday.
Osimhen registered just a single shot, that was off target and his performance was visibly affected by a previous muscular problem.
Remy replaced him just before the hour-mark, and it was revealed the Nigerian suffered a thigh injury which makes him a doubt for the match against Marseille next week.
Lille's medical staff will check the extent of the injury, but coach Christophe Galtier stated after the game he is hoping the injury isn't serious.
Osimhen's compatriots Samuel Kalu and Josh Maja were introduced as substitutes in the second half with the former coming on for Morocco's Youssef Ait Bennasser in the 64th minute while Maja replaced Guinea's Francois Kamano in the 74th minute.
The victory pushed Lille to third place in the Ligue 1 table while Bordeaux dropped to seventh after conceding their second straight defeat in the French top-flight.