Lambert was speaking after victory at Crystal Palace.
"If anyone wants to know about Roy, I'll put it on your plate so you know: there's absolutely no problem whatsoever," said Lambert.
Former Manchester United lynchpin Keane's party line for quitting his Villa post was to focus on his assistant's role with the Republic of Ireland.
Lambert added: "He's got a lot of commitments with Ireland, he's never had a break from going away with Ireland, and never had a break from Aston Villa. So I totally respect his decision.
"Contrary to reports, there was absolutely nothing, absolutely no bust-up, no arguing, nothing like that.
"I thank him for his time coming to work for me.
"Back to your point, it's a massive four points in the last two away games, and we're four games unbeaten.
"Two young centre-halves having played well, Benteke back in with a goal and I thought Alan Hutton was fantastic."
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