I got interested it this as the story seemed a bit vague. In 1850 when the Prince of Wales commissioned the building, Lilly Langtry was 4 years from being born. 27 years later on May 24th 1877 they actually met.
I must say that the future king had wonderful foresight to construct the "love nest" 27 beforehand. the little theatre might have been constructed during the affair, but it was not for her acting talents that the Prince was interested in her.
The following quote from Twilight of splendor: the court of Queen Victoria during her diamond jubilee year, Greg King, John Wiley & Sons, 2007 p.138 is self explantory:
"He once complained to her, "I've spent enough on you to build a battleship," whereupon she tartly replied, "And you've spent enough in me to float one"."