Grax cancelled out Dimitri Payet's opener with three minutes left after Lille failed to clear Stephane Darbion's cross.
Lille, who have not won since their opener at Saint-Etienne, are 11th with six points from five matches, six points behind leaders Marseille who visit Nancy on Sunday.
Bordeaux, who had a chance to climb to second, were held to a goalless draw at Valenciennes.
Sochaux moved off the bottom with their first win of the season at 10-man St Etienne, while fellow strugglers Evian Thonon Gaillard defeated Bastia 3-0 and Nice won 4-2 at Brest.
Lille, who host BATE Borisov in the Champions League on Wednesday, controlled the game but struggled to create any clear chances as the hosts forced them to rely on long-range attempts.
Payet had an effort on target in the 18th minute but his shot from 25 yards lacked power as did playmaker Marvin Martin's volley from a Mathieu Debuchy cross 10 minutes later.
Lille finally went ahead six minutes before the break when Payet netted from just outside the area but Grax popped up with a late goal to deny the visitors all three points.
However, the result did not stop Troyes slipping to the bottom of the table with two points.
Unbeaten Bordeaux's point at Valenciennes puts them fourth and they are now level on nine points with third-placed Paris St Germain who beat visitors Toulouse 2-0 on Friday.
Sochaux ended a run of four straight defeats with a shock 1-0 win at St Etienne who had full-back Jonathan Brison sent off for a rough challenge on Abdoul Camara after nine minutes.
Resilient St Etienne were beaten when Thierry Doubai netted a splendid overhead kick from just inside the box in the 75th.
Sochaux climbed one place to 19th on three points while St Etienne remain in ninth spot level on six points with Nice who hammered visiting Brest for their first win of the season.
Camel Meriem fired Nice ahead in the 46th minute before centre back Nemanja Pejcinovic doubled their lead five minutes later with a header from a corner.
Eric Bautheac and Valentin Eysseric then scored for the hosts in an action-packed second half with Brest replying twice.
Cedric Barbosa shone as Evian, who fired coach Pablo Correa 10 days ago with one point from their opening four games, got their first win this season against promoted side Bastia.
The 36-year-old playmaker netted a powerful header in the 36th minute to put the hosts in front and sealed the victory in the 78th, five minutes after Yannick Sagbo had doubled the lead.
Evian are 15th on four points while Bastia, who surprisingly won their first two games in the top flight, are 12th on six.
Second-placed Lyon host Ajaccio on Sunday after Lorient host Rennes in the early kick-off.
- Dimitri Payet