The Spurs are in total control. No, the Lakers won't be able to sign KL next season. They'll have no cap room if they get LBJ and other FA's to sign this off-season. KL's options dry up once the Lakers fill out their roster this off-season. Maybe the Clippers will have room but not the Lakers.
If LBJ picks the Lakers, he runs the show. He's not going to keep a max salary slot open until next season. He wants to win now and isn't interested in waiting a year.
It's very possible LBJ resigns with the Cavs. If that happens, PG probably stays in OKC. That likely means that the Lakers will be in full tank mode again this next season unless they decide to pursue other FA's this off-season.