Am not sure whether you're referring to the Business or First Class lounge, but either way I can't see you having any issues at that time. I regularly use the lounge at the peak of flight departures to Europe in the evening, and even then have always never had an issue finding a shower room post refurb.

From memory, there is body lotion and an EDT bottle in the shower room - I'll make sure I have a look when I'm travelling tomorrow evening.