I don't think it will have that name every time. I'm betting the f1 relates to the backup set and soon it will be f1d1, then f1d2,and when a new backup starts, but f2. But they should start with "LiteSpeed."
I would test this by running the Fast Compression script a few times on a small test database, then run the script with the @forcefull parameter uncommented to tell LiteSpeed to start a new backup set, and examine the logs in more detail.
--
David