Osimhen, who is having a season to remember thanks to his goalscoring exploits in Ligue 1, was handed his maiden appearance in the competition, but the Nigerian missed several scoring opportunities.
Quincy Promes headed the Dutch side ahead after 18 minutes before Edson Alvarez scored to put them two goals up five minutes after the interval.
Nicolas Tagliafico dented Lille's chances of launching a comeback with the hosts' third of the evening thanks to Hakim Ziyech’s assist.
Not our night in Amsterdam, but we'll bounce back. #AjaxLOSC #UCL pic.twitter.com/Ujqtsqa7KI
— LOSC Lille EN (@LOSC_EN) September 17, 2019
The Nigeria international was on parade for the entire duration as Andre Onana put in a fine shift to stop the Great Danes.
Following this defeat, Lille sit at the base of Group H and they would be seeking redemption when they welcome Chelsea to Stade Pierre-Mauroy on October 2.
Before then, they take on Rennes, Strasbourg and Nice in their next three French top-flight fixtures.
Osimhen boasts five goals in five league appearances to lead the goalscorers’ chart alongside Lyon’s Moussa Dembele.