Every update to a channel creates a set of onchain transactions that you need to store until the channel is closed.

These transactions are how you keep your channel partners honest. At the time of any update, both nodes of a channel exchange transactions that say, and I'm paraphrasing, "if I try to screw you using this point in our history, these transactions I've signed allow you to take all of my money from this channel." So you store those transactions in case they try to screw you.

It sounds like you're rubbing against some storage limits that Alby has and I'd guess that rather than give you unlimited storage Alby prefers nagging you about it.