The victory takes PSG to 13 points and above Monaco on goal difference although the principality side could restore a three-point lead when they travel to undefeated Nice on Wednesday.
"If we carry on like that, we'll get to the top," Lucas told French broadcaster Canal Plus. "It's only the beginning of the season but we're progressing and we have to carry on. We're reaching our level."
Unai Emery's PSG side took the lead in the 15th minute when Maxwell's cross looped over stranded goalkeeper Baptiste Reynet and into the net after a deflection off the unfortunate Lang.
Cavani doubled the advantage from the spot 12 minutes later with his sixth league goal of the season when Jordan Loties brought down Adrien Rabiot after PSG had opened up the visitors.
"We're disappointed, even if we know that we're not in the same category (as them) and that PSG are so far beyond us," said Dijon coach Olivier Dall'Oglio.
"When you come here, you know you're going to suffer, but there's still always this foolish hope."
Dijon's Mehdi Abeid struck the bar with a powerful strike from outside the area after 33 minutes in a rare foray by the visitors, while PSG had a penalty appeal turned down when Lucas was tripped on the edge of the area in the 56th.
Lucas added extra gloss to the scoreline 11 minutes later when Maxwell's excellent cross evaded Loties and the Brazil international was on hand to head past Reynet.
"My objective is to score as many goals as possible," Lucas said. "Everyone criticises me because I don’t score.
"I'm trying to be more efficient."
PSG's next opponents, high-flying Toulouse, beat Lille 2-1 away, with a double from the outstanding Ola Toivonen either side of Marko Basa's first-half effort for the hosts.
Toulouse moved up to third spot on 11 points.
There are eight Ligue 1 matches on Wednesday, with Olympique de Marseille hoping for a second victory when they visit Stade Rennes while Olympique Lyonnais host Montpellier.
(Reporting by Ed Dove; editing by Ken Ferris and Toby Davis)
