SQL Server recovery with LVM snapshot as base
Going from this: "I can at this point restore a full backup and recover with the logs, but I wondered if it was possible to skip the full backup/restore step and use the snapshot as a base?".

In order to restore the log backups the database needs to be put in a 'restoring' state. Now I'm not actually sure if you can put the online database in that state without actually making a real restore of a full backup. The normal way would be to restore the db from full backup using the NORECOVERY option (expects log backups) and then restore the following log backups.

I'm not sure if there's a way to circumvent it.

PS: Jack, you don't need to mark this as the answer yet, let's let the wiser SQL Server admins here speak their own experience, maybe I'm just plain dumb and missing something fairly obvious :-).