You play hardball with him. That is what you do.
If this Celtics-Clippers trade goes down, Chris Paul is likely to re-sign with the Clippers. Immediately, Atlanta is not an option for Dwight if Paul re-signs with the Clippers. Who's next, the Mavericks? What do they have? An aging Dirk? Cross out Dallas off the list. Houston? Ok. They are are only competition. But we can offer more money and Dwight loves Hollywood.
He can request a sign-and-trade all he wants, but if you are the Lakers, just play hardball with him. He cannot outright sign with the Clippers. They are not financially fit to sign him. He has to where to go. Lakers are going to be his only good option.
Of course you play hard ball. That's what you have to do at first.
I'm not saying Dwight requests a trade to the Clippers, I'm saying he tells the Lakers he will not re-sign with them. Which at that point, what do you do if you have that offer on the table and he is definitely not going to re-sign?
If Lakers don't sign and trade Dwight or re-sign him for themselves, he's walking to Houston. No doubt in my mind. No other team, just Houston.
Those are the three options, but if one of those options are not going to happen (him re-signing here), as a GM & Owner you NEED to explore all possibilities.