If I was an incoming GM to this team, I'd move Carter and Martinez. Clear out cap, get good young kids and picks.
I'd trade the entire middle class of the team that could be moved. Carter, Martinez, and the other three I mentioned. Toffoli isn't going to score all that many more goals per season, while his contract probably doubles. Pearson, same thing. Muzzin, if you're not competing, why keep him? Want to throw Lewis in there, that's fine too.
Kopitar, Quick, Brown, and Gaborik are untradeable for one reason or another. I guess you keep Doughty, but he's not going to get better while his price goes up in a few years either. Trade anyone else that's worth something, and keep these 4 or 5 around while their contracts slowly expire. By the time Brown and Gaborik are gone, the picks and prospects gotten for the other guys are coming up, hopefully with positive results. Then you have a young foundation to support an older Kopitar, Quick, and Doughty.
That's mostly video game stuff though. That much wouldn't happen in reality.
Of course if Gaborik were to for some crazy reason retire, that would help. If Vegas were to take Brown for another crazy reason, that would help. Failing that, we've got a good idea of what the team is in the last 224 games. With or without Quick in net.