Christophe Galtier's side, who have conceded only two goals this season, prevailed with efforts from Burak Yilmaz, Jonathan Bamba, Jonathan Ikone and Yusuf Yazici with Lens finishing with nine men after Jonathan Gradit and Clement Michelin were sent off after the break.
Lille have 17 points from seven games and lead second-placed Paris St Germain by two points.
Lens, back in the top flight after a five-year spell in Ligue 2, are fifth on 13 points.
They have not beaten Lille since 2006 in all competitions and it never looked like they were going to end a 14-match winless streak against their fierce rivals.
Lille went ahead after 11 minutes when Yilmaz headed home from Benjamin Andre's cross for his third goal of the season.
Lens went down to 10 men in the 58th minute as Gradit picked up a second yellow card, but the visitors had long lost the plot.
Ikone added a third with a low shot from just inside the box and Yazici rubbed salt into the visitors' wounds with a fourth, 11 minutes from fulltime, with the final goal coming after Michelin was shown a straight red card for a dangerous tackle in the 75th minute.