I don't know all the options, because I usually use the Lufthansa Lounge which is reasonable and has showers. It is open 24 hours. Ms. ParisMoskau used it once for an overnight stay that was too short to use a hotel in town, and found it bearable; it was almost empty overnight and she could move a couple of chairs together.

If your client can access the lounge that may work. I don't think there is a transfer hotel. Without lounge access I don't think it's fun.