Misconception #1: Lamoriello won't go out and acquire the 'big name' player.
I really don't understand why people think Lou wouldn't want a star player on his team, he has acquired many in his past.
A common theme with all of these thoughts will be "people don't remember when," the first one that I will bring up is when he traded for Ilya Kovalchuk from the Thrashers at the time. This was a star goal-scoring Russian machine drafted 1st overall in 2001 who was on an expiring contract, and he basically stole Kovalchuk from Atlanta.
He acquired Kovalchuk for a few players that were not very impactful in the NHL and a first and second-round pick. Yeah, steal is the right word.
Kovalchuk was one of, if not the, most significant acquisitions Lou has ever pulled off, but of course not the only one. In fact, he's one of the biggest reasons that Russian players were allowed to come to North America to play in the NHL. In his early days with the Devils, he sought out superstars playing overseas even when they weren't allowed to play in the league by government authority. He was successful and showed his commitment by bringing over star Soviet Union defenseman Slava Fetisov in a potentially dangerous situation for all parties involved.
RegardingWhen it comes to the Islanders, fans always wanted an exciting, high-upside goal scorer to alleviate all of the team's scoring issues. Considering Lou has stated that he expects to make some "hockey trades" this offseason, we could see a name like Vladimir Tarasenko in rumors as we did last offseason. There are also rational UFAs that he can acquire, an example being someone like Filip Forsberg.
Other big-name players Lou has acquired in the past include Alexander Mogilny, Joe Nieuwendyk, Scott Stevens, Doug Gilmour, Peter Stastny, Dave Andreychuk, among others. But what is it that they all have in common? They are all established Hall of Fame players. Those are all very talented offensive players during their careers, which goes to show why people have the wrong idea over my next point as well.