Couple things wrong with the "designated player" talk...
First, it's only for rookie scale extensions. So Dame is our "designated player" who can receive a 5-yr extension on his rookie scale contract for the max. So while Dame is in his contract, we can't have another rookie signed to a 5-year extension. (Meyers could only get 4, same with CJ, same with Plumlee). It's not for a contract signed after your contract ends, and you're RFA. Jimmy Butler, for example, is not going to be a "designated player" even though he's getting a 5yr contract coming off of rookie scale.
LMA's contract a) isn't an extension, and b) isn't coming off a rookie scale contract. So he could sign a 5yr contract today.