I've used a lot of lounge showers. I've never seen one that didn't provide amenities, that didn't provide towels, or that didn't clean up between users.

Lounges vary in their procedures for showers: hand you a key, escort you to the shower you should use, etc. Procedures can also change depending on how crowded the lounge is, both in terms of shower usage and in terms of other demands on staff time. Ask at the desk when you check in. Even if you don't want to shower right away, if there's a line, it can help to get your name down right away.