Yes.

However, this can be solved by services giving users the ability to migrate their account to a different LN wallet. Should be as easy as being logged in and just going to your settings to link another LN wallet. Then you can login to the same account using both wallets. Deleting the old linked wallet would then finalize the migration.

However, SN is guilty of not having this, too. But there is already a ticket.

Thanks for posting, this brought the importance of this ticket back into light!