I can say that the Holmes Place Urquinaona fitness centre is a first rate club, better than most in the US and more on par with something like Crunch or Equinox. I'm guessing that the LM BCN would have a partnership with the location a bit closer,
Holmes Place Balmes club, which is about 5 blocks from the hotel at , 44-46 Balmes.
If you are a Platinum member they shouldn't charge, and if you are arriving early they might prefer to give you a pass as a way to hold off on the room being ready.