Lamoriello, 75, will be general manager, but the Islanders have not replaced Weight. Barry Trotz resigned as coach of the Washington Capitals on Monday, 11 days after guiding them to the first Stanley Cup championship in their 43-season history.
John Tavares can become an unrestricted free agent July 1, although it has been reported that Lamoriello and the 27-year-old franchise center have been talking on a regular basis.
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"Hey, Lou has done a great job everywhere he has gone," Barzal said Tuesday at NHL Awards Media Day. "Obviously, I love Dougie, he was great for me, gave me lots of opportunities, and Garth drafted me and I have ties to him as well.
"Again, Lou's in charge and he has done a great job everywhere, so obviously I have faith in him to do the same here."
What happens with Tavares, who has been with the Islanders for nine seasons since being the No. 1 pick in the 2009 NHL Draft, will go a long way toward shaping what the 2018-19 season looks like for the Islanders. Tavares had 84 points (37 goals, 47 assists) this season, second on the Islanders behind Barzal, who had 85 (22 goals, 63 assists) to lead NHL rookies.