I'm pretty sure, although I am usually in the Senator lounge. I've only been in the Business lounge twice since it was converted (it used to be the LH Senator Lounge, and didn't see a shower. Both are small - there's certainly no place to put a shower.

There certainly are no restrooms - one uses the quasi-public ones across from the BA lounge which are a little nicer than the typical ones in GVA. I am absolutely certain of that.

It might be that the lounges have some sort of arrangement by which you don't have to pay for an otherwise-public shower.