It's barely farther in LHR but you do have to leave the lounge to go there; the spa (and its associated showers) are between the CCR and GF entrances.

If one had possessions set out or luggage, a travel companion holding the boarding passes and a morbid fear the lounge staff might not recognise a passenger who left the lounge a minute earlier saying "I'm just going to the spa, back in a minute", a desperate need to pour LPGS or G&T into one's mouth, etc, - these might impede going there and asking in person.