The midfielder, who is currently on loan with Oldham Athleitc from the Canaries, was visibly angered and upset by comments made by a certain section of Liverpool fans during his side's 5-1 loss.
The matter is now being handled by the police and Liverpool, something that Lambert believes is encouraging.
"I spoke to him last night after the game," said Lambert. "I can't comment on what actually happened, but Tom himself, which is the most important thing, is okay.
"What we said will remain private, but he is fine, which is the main thing for me.
"He is okay, which is pleasing, but I am sure Liverpool Football Club will do it properly, investigate what has happened."
Lambert's Norwich beat Burnley 4-1 in the FA Cup this afternoon.