The Argentine forward, who had previously netted four league goals this season, struck twice in the first half and again after the break. Edinson Cavani, with a double, and Maxwell completed the rout.
Lille, who grabbed a consolation goal through Marko Basa in the 59th minute, finished with 10 men after Sebastien Corchia was sent off in the 72nd.
PSG have 68 points with five matches left, three ahead of second-placed Olympique Lyonnais who have played the same number of games and travel to Stade de Reims on Sunday.
Laurent Blanc's PSG, knocked out by Barcelona in the Champions League quarter-finals in midweek, were 2-0 up after four minutes.
Italy international Thiago Motta was back after a long injury layoff and he made his presence count, marshalling the midfield.
In the first minute full back Maxwell latched on to Serge Aurier's cross to open the scoring and three minutes later Cavani netted with a fine lob after being set up by Javier Pastore's defence-splitting pass.
Motta then played in Cavani in the 28th minute and the Uruguay striker crossed for Lavezzi to fire the ball under Vincent Enyeama's bar.
One minute before the interval Lavezzi was at it again, tapping in from close range after Blaise Matuidi's centre.
Defender Basa headed in a Lille corner in the 59th minute but the northerners, who are eighth on 50 points, had long given up hope.
Things got even worse for the visitors when Corchia held Lavezzi's shirt in the box and was shown a second yellow card. Cavani converted the resulting penalty.
Lavezzi wrapped it up in the 77th minute with a low cross-shot after being set up by Pastore.
(Editing by Tony Jimenez)
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