Quoting: TJTwolf
Hard to see the real gain here for the Islanders. Mayfield is a RHD who can they easily re-sign or replace. Bjornfot is a LHD who has 'struggled to crack the LA line up' but is now being used out of position on the right. Valamov's cap space will be invaluable, especially with Horvat's and Barzal's extensions kicking in next year, so replacing it with another duff goalie in Petersen is a poor idea. In a worst case scenario they re-sign Schneider and bring him up as a cheap veteran back-up, and there are likely other candidates in the off season, or they even re-sign Varly to a cheap deal. Lemieux is, as you say, a throw in, and guys who could fill that 4th line role are easily acquired in free agency, and probably acquired cheaper. So for taking on cap (that they will definitely need next year) they get a 2nd and a 3rd.
LA however benefits in escaping Petersen's cap hit and adds Mayfield who they can re-sign to give them good RHD depth. I wouldn't call it stupid but it certainly seems to be more beneficial to the Kings than the Isles.
It's possible the Isles miss the playoffs but they're still in contention at present albeit likely only in the battle for a wild card spot. They added Horvat with that in mind so can't see them keen to quit on the idea.
Almost everything you say here about the Kings is factually inaccurate.
First, Bjornfot is not playing on the right side. You might be thinking of Durzi, who is a RHD, being used on the left. Bjornfot is currently the 7th defenseman, and he takes turns with Alex Edler at 3LD. He's only 21 years old, and has a bright future ahead of him with the Kings. They have no interest in trading him.
RHD is the Kings single strongest position. Mayfield would be, at best, 6th on the LA Kings RHD depth chart behind Doughy, Roy, Durzi, Clarke, and Spence. The Kings also have Sean Walker and Helge Grans that are RHD that would probably fall in behind Mayfield.
Petersen looks really good in Ontario right now. The Reign have the single best combined save percentage in the AHL between Villalta and Petersen. They have no reason to dump Petersen's contract. He'll be back in the NHL next season.
There is no reason at all for the Kings to do any of this.