Les Gones had the opportunity to go five points clear of nearest challengers Paris St Germain, who travel to Bordeaux on Sunday, but a combination of poor finishing and several fine saves from Evian goalkeeper Stephan Andersen ensured the spoils were shared.
It was a much-needed point that took the visitors out of the relegation zone, but Lyon will be wondering how they did not come away from this match with all three points.
Coach Remi Garde urged his side not to get "drunk" on their standing at the top of the league and it seemed his players had not taken the words on board in a lifeless opening.
Milan Bisevac brought the game to life however, with his powerful header from Yoann Gourcuff's corner forcing the first of several fine saves from Denmark international Andersen.
In what would prove to be a rare foray into Lyon's half, Yannick Sagbo saw his header kept out by Lyon goalkeeper Remy Vercoutre.
The hosts moved up a gear, with both Gourcuff's fantastic 25-yard free-kick and Michel Bastos' low drive from the edge of the box fantastically denied by Andersen.
Alexandre Lacazette had a marvellous opportunity to break the deadlock after the interval, but after being picked out at the far post following some good work down the left by Steed Malbranque, the unmarked France Under-21 international struck wide.
Former Charlton and Brondby goalkeeper Andersen was once more required to keep the scores level with another brilliant stop from Lisandro Lopez's effort.
Clement Grenier fired over from just outside the box, but Lyon were unable to fashion any meaningful chances in the closing stages as Evian's defense held firm.