Keane surprisingly stood down as assistant manager at Villa Park last week, just five months into the role.
The former Sunderland and Ipswich Town boss cited difficultly between combining his Villa role with his position as Republic of Ireland assistant manager to Martin O'Neill.
However, there have been reports that Keane was involved in a training-ground row with senior players at the club.
But Lambert stressed that was not the case after Villa's 1-0 win at Crystal Palace in the Premier League on Tuesday.
"There's absolutely no problem whatsoever he has a lot of commitments with Ireland," Lambert said.
"He's never had a break from going away from Ireland or with Aston Villa. Contrary to reports there was no bust-up, no arguing, nothing like that.
"I thank him for his time, coming to work with me in that spell.
"I spoke to him before the Burnley game and after the Burnley game and our relationship is the same. I want to put that to bed."
