Lou Lamoriello always believed the Islanders’ new arena at Belmont Park would become a reality. It’s likely he would never have agreed to become the team’s president and general manager in 2018 otherwise.

Still, Lamoriello knows how significant it is for the organization that the $1.3 billion arena and entertainment plan received its final approval from the state Franchise Oversight Board on Tuesday after the Empire State Development board voted on Aug. 8 in favor of the project.

“You know how big it is,” Lamoriello told Newsday on Thursday. “Without a new arena, there would not be the Islanders on Long Island. I think that says it all.”

Lamoriello was able to re-sign the team’s key unrestricted free agents this offseason except for goalie Robin Lehner and third-line center Valtteri Filppula. The previous summer, former captain John Tavares left for his hometown Toronto Maple Leafs for a seven-year, $77 million deal that was less than the Islanders offered.

The Islanders will continue to split games between NYCB Live’s Nassau Coliseum and Barclays Center in Brooklyn for a second straight season. Their new building is scheduled to open for the 2021-22 season and Lamoriello knows uncertainty about the Islanders’ arena situation was a factor when talking to free agents.

“I think that’s always something behind someone’s mind, including our own free agents,” Lamoriello said. “But they have the confidence in believing in our ownership’s commitment to getting the arena.”

Lamoriello was able to re-sign unrestricted free agents Anders Lee (seven years, $49 million), center Brock Nelson (six years, $36 million) and right wing Jordan Eberle (five years, $27.5 million).

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Restricted free agent forwards Anthony Beauvillier, Michael Dal Colle and Josh Ho-Sang remain unsigned. But Lamoriello said agreements are in place with two of them.

“None of our restricted free agents will be an issue, we’ll have everyone signed,” Lamoriello said. “A couple of them have already agreed, it’s just getting everything executed.”

Beauvillier, who played center in junior hockey but has played almost exclusively on the wing as a pro, is among the potential replacements for Filppula. Lamoriello also included Tanner Fritz, Otto Koivula and college signings Mason Jobst and Bobo Carpenter as those who could compete for the role.

But he did not place Casey Cizikas, who scored a career-high 20 goals last season, on the list because Lamoriello believes coach Barry Trotz will want to keep the invaluable fourth line of Cizikas with Matt Martin and Cal Clutterbuck intact.

“I don’t think Barry would want to tinker with the Cizikas-Martin-Clutterbuck line, he feels very strongly on that,” Lamoriello said.

Clutterbuck is recovering from offseason back surgery and Lamoriello said both he and left wing Andrew Ladd, who had surgery to repair a torn anterior cruciate ligament in his left knee, have resumed skating.

Lamoriello said Ladd “will be a little longer than Clutterbuck,” and he expects Clutterbuck to be ready for the start of the season.

“I do not foresee any issues for the latter part of training camp, the beginning of the season,” Lamoriello said.

Lamoriello said he also expects to bring at least one player into training camp on a professional tryout offer and did not rule out further personnel moves, either via free agency or trade.

“What we don’t want to do is overstock what we have,” Lamoriello said. “If we can pick the right kind of player that can complement, or we can complement him, we’ll do it.

“We also have a couple of excellent young players,” Lamoriello added. “We’re going to have to wait and see where they’re at. Because they’ll force us to make some decisions on all the players, who will be able to bring players in return in a trade.”