"LOSC strongly condemns the unacceptable behaviour observed, as well as the hateful comments and racist insults made by certain individuals in the visitors' section during trips to Belgrade and Strasbourg last Thursday and Sunday," the club said in a statement.
"Such behaviour is unacceptable and completely contrary to the values that the club consistently upholds and promotes."
The statement came after testimonies and video footage circulated on social media showing some Lille fans shouting racist remarks in Sunday's 2-0 loss at Strasbourg in Ligue 1.
Lille lost 1-0 at Red Star in the Europa League.
"Concrete measures were taken this morning. A procedure to identify the individuals involved is currently under way, with a view to filing several complaints with the police authorities," the club added.
"LOSC intends to pursue legal action against them and seek appropriate sanctions."