Kante suffered an injury while warming up ahead of France's Euro 2020 qualifier against Iceland last Friday, a game his nation went on to win 1-0, and the midfielder then sat on the bench during France's 1-1 draw with Turkey on Monday. The injury has ruled the 28-year-old out of his club's Premier League match against Newcastle this Saturday.
France manager Didier Deschamps said earlier this month: "Frank rang to ask me not to pick N'Golo for last month's matches. Fine, but sometimes it should go the other way too ... I have two important matches coming up, maybe I should ask him to play Olivier [Giroud] more!"
But Chelsea boss Lampard said on Friday that communication from France's side could have been better.
"We all have our selection problems, but the Kante one was not a laughing matter," Lampard said.
"It was clear that he wasn't fit to play the [Turkey] game and he sat on the bench.
"I think it could have been handled better. It was clear that he wasn't fit.
"Things weren't coming back to us as we expected them to come back. I understand when players are on international duty they're [the nation's] players, but ... I would always try to have open lines of communication with an international manager."
Lampard also said midfielder Mateo Kovacic is in contention to play against Newcastle, with the Croatia international having trained this week.
He added that Ross Barkley is "fine" after the England midfielder picked up a calf issue against Bulgaria this week, and that defender Andreas Christensen will likely be out for another two weeks with a hamstring problem.
Antonio Rudiger is also progressing towards a comeback from injury, according to Lampard.