Lightning Addresses aren’t a thing it’s just a construct on top of a LN node. (Just have to mention that. There shouldn’t be any reason that you can’t keep your existing lightning address with a new node backend… except for the fact that most lightning addresses are custodial situations)

If you can completely deplete the balance you can go for that, and wait for your counterparty to close the channel for you. You might be given some dust back whenever they decide to close it.

Sometimes it is difficult (with liquidity being depleted on the side of the counterparty) to fully drain, and in that case closing the channel might be better.