A dismal run of form has piled the pressure on Celtic boss Lennon and, despite a spirited display from his youthful side, it looked as though they would be extending their winless run to six matches.
Timothy Weah's maiden Lille goal – a fantastic volley from just inside the area – had made it 2-2, cancelling out Callum McGregor's first-half penalty, which came at the end of a frenetic seven-minute flurry in which Christopher Jullien and Jonathan Ikone also netted.
Lille looked well placed to push on and seal a win which would have seen them top Group H when Weah, son of Liberia legend George, struck against his former club, yet Turnbull's neat finish in his first European appearance secured a hard-fought Celtic triumph.
Celtic had the lead after 21 minutes – Julien heading in from Turnbull's fantastic left-wing corner.
Yet their advantage lasted under three minutes, with Yusuf Yazici taking advantage of McGregor's mistake by squaring for Ikone to tuck in.
Domagoj Bradaric's clumsy tackle on birthday boy Jeremie Frimpong gifted Celtic the opportunity to restore their lead, though, as McGregor atoned for his error with a composed finish.
McGregor got lucky when he diverted Cheikh Niasse's cross off Conor Hazard's left-hand post, before Turnbull saw a close-range shot deflected wide at the other end.
But Lille had a second equaliser when Celtic failed to clear a free-kick and Weah lashed in on the volley.
Celtic did not let their heads drop, though, and Turnbull was on hand to sweep home from Kristoffer Ajer's cross with 15 minutes remaining – Isaac Lihadji subsequently squandering a golden chance to snatch a point for Lille.