Kiwi Gatland is repeatedly linked with the All Blacks top job that will be vacated by Graham Henry after the tournament.
Wales are currently one win away from reaching their first World Cup final, with Gatland already tied in to a new four-year deal that will incorporate the 2015 competition hosted by England.
It is a contract that Welsh Rugby Union group chief executive Lewis describes as "watertight."
"Having worked in the music business for so long, when stars break and you sell millions of records and generate hundreds of millions of pounds, you have got to make sure you have got a contract there that is watertight," he said.
"And we have got a watertight contract.
"Even if anyone wanted to come and have a conversation with us, and I am not suggesting this at all, it would cost them a heck of a lot of money."
It was four years ago this week that Lewis first met with Gatland at Auckland Airport, their initial talks coming soon after Wales crashed out of the World Cup against Fiji, a defeat that resulted in Gatland's predecessor Gareth Jenkins losing his job.
"It all fell apart in Nantes, and I said immediately then that we had to stop and change," Lewis added.
"I got the backing of the (WRU) board to say we had to change, change radically and start searching around. We spoke with Jake White, we spoke to some coaches in England as well.
"And down here in New Zealand, I arranged to speak with Robbie Deans, Warren and Ian Foster. The All Blacks had played their World Cup quarter-final by this stage and lost to France.
"When I met Warren, and people didn't believe me at the time, I knew virtually in the first part of our conversation. I realised he would fit with us.
"I had done my homework beforehand - I had talked to the rugby specialists. I rang up lots of people in the game who I trusted, who knew their rugby, who had either played it or observed it.
"I spoke to people in Ireland and England, and I also spoke to a number of players. I had identified what was required.
"Warren ticked all the boxes from the rugby side, but most importantly I had identified what was required culturally.
"As soon as you met him, you realised 'he's one of us.' Welsh-New Zealand, blue collar, working class, straight talking, likes to have some fun but knows there is a line where you say 'stop now, it's work time.'
"We work, work, work, work, and then we will have a couple of beers. I just felt it talking to Warren that he got it. He was the only guy we made an offer to."
Gatland had already won Premiership titles and Heineken Cups with Wasps, and Lewis felt he was the perfect fit to mastermind a Welsh revival from the depths of a humiliating World Cup exit.
"Warren, without doubt, was the key pillar in our strategy," Lewis added.
"There are a number of other pillars as well, but Warren heading up the national team, which is the machine that drives the enterprise forward, was key.
"Warren is like a great producer. The team are the stars, but you need someone there who is your great producer or director. He is our Steven Spielberg."
And as for Gatland's new contract, which was announced well ahead of the current World Cup campaign starting, Lewis said: "It felt right.
"I discussed it (new deal) with Warren and then presented it to the board.
"Understandably, some of the board were saying shouldn't we wait, but I said I didn't think we should wait. We had to be thinking of the next four years."
Gatland won a Six Nations title and Grand Slam during his first season at the helm, and now a World Cup final place will be secured if Wales can see off France at Eden Park this weekend.
"Everyone involved in Welsh rugby, from the grass-roots to the elite end, should feel so proud of what these boys have achieved. It is absolutely extraordinary," said Lewis, of Wales' World Cup campaign.
"They have been great ambassadors for Wales and Welsh rugby. What they are doing on the field has been matched by how they conduct themselves off the field.
"They are an incredibly mature group of individuals. This is the new generation, not only for Welsh rugby, but for Wales.
"They are talented and gifted, they are disciplined and hard-working, and they have got the mental toughness that people said that perhaps Wales haven't had in the past.
"All of Wales can be truly inspired by them, and we have to pay tribute to the coaches, management and back-room staff who have created this environment for the players to grow and flourish.
"This is the culmination of years and years of hard work from lots of people. It has been a huge team effort.
"We wanted to reaffirm Wales' reputation and standing, both on and off the field."
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