Bowkett claimed at a Norwich fans' forum on Thursday night that Lambert was asking for £2million compensation for unfair dismissal and breach of contract under the terms of his deal with the Canaries.
He reportedly said the manner of Lambert's departure was "no surprise because he has walked out on every club he has ever managed".
But Lambert has also 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 is disappointed Bowkett has decided to bring the issue into the public domain.
He 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."
Lambert would prefer to concentrate on Sunday's Premier League encounter at Tottenham when he has to decide whether to restore former Spurs striker Darren Bent to his starting line-up.
Bent admitted to being disappointed at being left out of the starting line-up against West Brom but responded in the right manner by coming off the substitute's bench to score the equaliser in a 1-1 draw.
Lambert is adamant there is no problem with the England forward who has netted in his last two league games.
He said: "If I could pick everyone I would but I can't and I just try and pick a team which might get a result.
"I understand people's frustration (at not playing) but I try and honestly select the team.
"Some of the best players in the world have been left out, Messi, Rooney, Ronaldo. I dropped Grant Holt last season at Norwich.
"If you are going on about Darren, I don't have one problem whatsoever.
"He didn't knock on my door. That's why I don't think there is a problem. I'm pretty sure if Darren has a problem he would come in and see me and he hasn't.
"He did brilliant when he came on, he scored and his finish was brilliant."
Lambert is impressed with the way Andre Villas-Boas has maintained Tottenham's fortunes after the departure of Harry Redknapp as highlighted by last weekend's away win over Manchester United.
He said: "Tottenham had a strong squad when Harry had them and Andre has taken them on.
"There's not many teams who go to Old Trafford and win that's for sure. It was a massive result for them.
"After Harry Redknapp left it was a massive job for someone given his record.
"But Andre is not a novice. He's won the Europa League with Porto and some big trophies so I'm pretty sure he could have handled it."
Lambert has no fresh injury concerns with midfielder Stephen Ireland (broken arm) and defender Richard Dunne (groin) still ruled out.