Villeneuve, the outspoken 1997 world champion, called Verstappen "a child" after the Dutch driver threatened to "head butt" journalists in Montreal.
However, it was subsequent comments by Lauda that really got Villeneuve fired up.
Lauda, a contemporary of F1 legend Gilles Villeneuve, said that the famous Canadian racer was a lot like Verstappen.
Jacques, Gilles's son, reacted angrily to that comparison.
"Maybe Lauda is still dealing with Ferrari's decision to replace him with my father," he told Le Journal de Montreal.
"I agree that Verstappen takes risks like my father did, but there is a big difference - my father had respect for his opponents and learned from his mistakes.
"He had a completely different upbringing. Quite frankly I don't understand the comparison at all."
The 2018 calendar continues with the French Grand Prix next weekend.