Lambert angered Norwich with the manner of his departure to take charge at Villa Park in June and the aftermath has now brought legal action from both parties.
Norwich chairman Alan Bowkett claimed at a supporters' meeting on Thursday that Lambert was asking for £2 million ($3.2 million) compensation for unfair dismissal and breach of contract under the terms of his deal with the Canaries.
Bowkett was also reported to have said the manner of Lambert's departure was "no surprise because he has walked out on every club he has ever managed".
But Lambert hit back on Friday as he revealed Norwich, who he led to two successive promotions, are also suing him over his departure.
A Premier League managers' tribunal is due to decide on the matter and Lambert said: "I'm disappointed what senior officials at Norwich have said in relation to myself.
"What Norwich haven't stated publicly is that they are actually suing me.
"I'll let him (Bowkett) say what he has got to say and we'll see what happens.
"It is before the Premier League managers' tribunal at which the LMA (League Managers Association) are acting on my behalf.
"That's the way it is at the moment and it is inappropriate for me to comment anymore and be disrespectful to the tribunal.
"I don't know when it is going to happen. I'm too busy trying to win games to worry."