The northeners, who were last champions in 1954 and won the French Cup on Saturday, have 72 points with two games left and lead Olympique Marseille by six points with a much better goal difference.
In Wednesday's other game, Paris Saint-Germain lost 1-0 at Girondins Bordeaux and missed an opportunity to leapfrog Olympique Lyon into third place, jeopardising their chances of a place in the Champions League qualifying round.
PSG, who have 58 points, trail Lyon by two points. The result means that Marseille are now certain to finish in the top three.
At Villeneuve d'Ascq's stadium Nord, where Lille play their home league matches, the hosts dominated throughout but had to stay patient.
"It's not done yet, but it looks very good," Lille midfielder Rio Mavuba told French TV channel Canal Plus.
"Hats off to the players, who put up a great performance four days after the (cup) final," coach Rudi Garcia added. "If we manage to do it, it will be huge."
Defender Franck Beria said Lille would not celebrate the title before it was officially sealed.
"We must show respect to our opponents because it's the way the club is," he said.
Gervinho came close in the 17th minute after collecting an Eden Hazard cross, only for his attempt to shave the post.
GOLDEN OPPORTUNITY
Two minutes later, the Ivory Coast striker missed a golden opportunity to put Lille ahead when he burst into the box, dribbled past Teddy Richert but skied his shot over the bar.
At half-time, club president Michel Seydoux strolled towards the stands with the French Cup trophy Lille claimed by beating PSG in the final.
After the break, Rudi Garcia's side continued to push hard and the Sochaux defence eventually cracked in the 53rd minute.
Moussa Sow, the league's top striker with 21 goals, set up Gervinho with a through ball for the slender striker to beat Richert with a low cross shot.
Lille then controlled the game with keeper Mickael Landreau enjoying a quiet evening.
At Bordeaux's Chaban Delmas stadium, PSG coach Antoine Kombouare surprisingly decided to leave France striker Guillaume Hoarau and former French international midfielder Ludovic Giuly on the bench.
It started badly for the visitors when, in the sixth minute, Zoumana Camara fouled Benoit Tremoulinas in the box.
Cheick Tidiane Diabate converted the resulting penalty and Kombouare waited until 10 minutes into the second half before sending Hoarau on to the field.
He made an immediate impact but his header was superbly tipped away by Cedric Carrasso who made another stunning save from a Nene free-kick.
"It's not the first time we miss such an opportunity," Nene told Canal Plus.
"Missing such a chance, once again, is really tough. Mathematically, it's not over, but it will be very complicated.
