We just don't know, we can only hypothesise. I don't believe that they were lovers, I don't think that Elizabeth slept with him or anyone else as she knew that her reputation had to be completely unblemished and she just could not risk pregnancy or scandal. Some suggest that she was actually physically unable to have a sexual relationship, others suggest that it was psychological, but I think it was a decision that she made, the decision to always be in control.
Others disagree and you can read a wonderful article by author Jeane Westin at https://www.elizabethfiles.com/did-they-or-didnt-they/3099/