A powerful free kick from Michel Bastos on 74 minutes cancelled out Cedric Barbosa's 57th-minute opener to move Lyon onto seven points from three games, one ahead of Marseille, Bastia and Bordeaux, who all play later this weekend.
Evian, who finished ninth last May, won their first point of the season.
Lyon had the control of the game until Evian took the lead when Barbosa chested down a Yannick Sagbo cross to shoot past France goalkeeper Hugo Lloris.
The seven-time French champions then upped the tempo and levelled thanks to substitute Michel Bastos, who already gave them the lead last week when they came back in the second half to thrash promoted side Troyes 4-1.
The Brazilian, who has been linked to Emirati club Al Ain for weeks, netted when he netted the free kick from 25 metres.
Both sides had chances to score a late winner but lacked the cutting-edge.
Defending champions Montpellier, who have only one point from two games, host Marseille on Sunday.
Paris St Germain entertain Bordeaux later the same day without their two biggest transfer window signings, Zlatan Ibrahimovic and Thiago Silva, who are not fit.
Bastia, who were promoted from Ligue 2 last May, could climb to the top spot after three games if they win at Stade Rennes on Saturday.
- Michel Bastos