They remain unbeaten after eight matches this season though and are only behind reigning champions PSG on goal difference.
Patrick Vieira's Nice sit fifth, four points off the early pace after PSG's 4-0 thrashing of Dijon on Saturday.
The best chance of the first 45 minutes fell to former Manchester United player Morgan Schneiderlin, but the Nice midfielder's header was brilliantly saved by Lille goalkeeper Mike Maignan.
Kasper Dolberg put the hosts ahead less than five minutes into the second half, getting in front of Lille defender Domagoj Bradaric before dinking a cool finish into the net to score his third goal of the season.
The away side levelled in the 58th minute as Luiz Araujo's excellent pass freed Burak Yilmaz, who hammered home a fierce volley.
The veteran Turkish striker has netted four Ligue 1 goals since signing from Besiktas in the close season.
Later on Sunday, slow-starting Lyon and Monaco go head-to-head at the Groupama Stadium.