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.
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."
"We must show respect to our opponents because it's the way the club is," he said.
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.
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'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.
