He said he expects dialogue between his agent, Neil Sheehy, and Lamoriello to intensify in the coming weeks.
"Neil's been out here a bunch this year, and his conversations with Lou will continue," the 28-year-old forward said. "They'll pick up here now and we'll go from there. Lou and him will get together and have their conversations, and then we can move forward. Nothing's really changed."
It's the second straight season the Islanders will have their captain potentially become an unrestricted free agent; John Tavares, who Lee replaced as captain, signed a seven-year contract with the Toronto Maple Leafs on July 1, 2018.
"You wouldn't and could not find a [better] captain," Lamoriello said of Lee. "He did a tremendous job. As I've said all along, we're going to do everything we possibly can to keep him. That's the best way I can answer that."
Lehner agreed to terms on a one-year contract with the Islanders on July 3, 2018, looking to start over after discussing going to rehab to help deal with mental health struggles that led to suicidal thoughts and drug and alcohol addictions.
The 27-year-old goalie went 25-13-5 with a 2.13 goals-against average, .930 save percentage and six shutouts in 46 regular-season games. He is a finalist for the Vezina Trophy, awarded to the top goalie in the NHL, and the Masterton Trophy, awarded annually by the Professional Hockey Writers' Association to the player who best exemplifies the qualities of perseverance, sportsmanship and dedication to ice hockey. The winners will be announced at the 2019 NHL Awards presented by Bridgestone at the Mandalay Bay Events Center sports and entertainment complex in Las Vegas on June 19.
"I can't say enough, I love this team," Lehner said. "I love everything about [it]. I've been very vocal about the situation here, but you never know with sports. I can only hope [I'm back]. We'll see what happens. I don't want to [tick] anyone off.
"I've got to kind of digest everything and see where everything's at. Obviously I'm happy I'm here and I'm feeling good. I'm happy, but there's a long road left for me to walk. I'm just going to try to find some type of stability moving forward."
Eberle had 37 points (19 goals, 18 assists) in 78 games, his fewest in a full NHL season. He scored in each of New York's four games during its sweep of the Pittsburgh Penguins in the first round but had three assists in four games against the Hurricanes. He turns 29 on May 15.