The story is written really well, but there is some things that make it really off. It seems like this was written as a sister/brother story, so that would play a big part in why there is tension between the MC and Lillie, especially the thoughts of the other one being with someone else and their actions a little better.
I think I understand what the writer was trying to convey in the story with Liam, even though I think he has to much of a 50 shades vibe going on. He is getting Lillie to be more open about the BDSM lifestyle, while she is still thinking of the MC as it is happening. I also think he is also suppose to be the release for her building sexual frustrations for the MC, until the MC mans up and takes a more dominant role. The problem is that it is way to fast paced, which makes people hate Liam, and think Lillie is nothing but a whore/slut, ready to do anything he wants on the first date after just a couple of encounters with great tips. In the current build of the game, she is not any better than the blonde bimbo that the MC can have sex with. Which puts some people off since she is one of the main characters for the MC to be with, if not the main.
If you do want to keep the characters and everything, instead of doing 2 different versions, just change the pacing and arc of Liam. Pacing and choices could fix it for people on both sides of the fence.
As an example of what could be done: If she is written to be a submissive pet, like it seems, you could have a story of him talking to her, feeling out what she likes, telling her what he like, maybe do some play stuff, build up from there, then have the choice if it gets full sexual or not.
But this is just my opinion, good luck, I can't wait to see what she comes up with if the 2 of you decided to change it.