The myth that Richard was a homosexual was invented in the 20th century. There is no historical evidence for it.
It was from various writings I’ve seen over the years and from a docent’s description of Richard’s life, which I saw in a special a number of years ago. I looked it up in Google and found the following. (I’m not trying to impugn him one way or the other. It’s difficult to “know” anything for certain about historical figures because their enemies generally outlive them. For example, it’s almost impossible that Marie Antoinette said, “then let them eat cake” as she would have been nine when she was supposed to have said it.)
https://www.google.com/#q=richard+the+lionheart+homosexual