The French champions had opportunities, but lacked sharpness against the German side who had United States men's national team defender John Brooks sent off shortly after the hour.
All four teams in the group have one point after Sevilla FC and FC Salzburg drew 1-1 in Spain earlier on Tuesday.
Wolfsburg enjoyed plenty of possession but failed to manage a single attempt in the first half as Lille threatened on the break.
Jonathan David found the back of the net three minutes into the second half after Jonathan Ikone had headed the ball down into his path, but the goal was chalked off after a VAR review ruled that it had previously gone out of play.
Lille continued to push and Angel Gomes had a golden opportunity before the hour, only for the English striker to sky his attempt over the bar.
In the 63rd minute, Brooks picked up a second yellow card for handball but Lille, who have taken only five points in their first five Ligue 1 games, failed to take advantage.