So my (massively overthought) theory for Lily is that she is a very multifaceted character, and the rolling stuff is partly true.
The status stuff is true, she wants to be known/popular, she likes attention (she is a stripper after all), she seems somewhat excited about Tremolo's dick being shared around
She has a soft, caring side; she wants to work in healthcare, regardless of if you've interacted with her before she defends/supports Derrick's post on Rooster, she immediately runs to help Tremolo after he headbutts someone's bottle, she comforts him when he's tripping balls
I also think she has a plan, strip at the club, make her money, get her degree, bounce.
At the HOTs party, she sees her opportunity to get with a Dik who is in ascendcy, Tremolo is gaining a reputation, his dick size (even if you're on a monk run up to that point) is basically a campus fact at this point, this leads into the status thing. But Tremolo is also known as a good caring dude at the same time, even on Dik runs. She thinks she can get with a hot dude with a tree trunk, stay reserved emotionally and stick to the plan.
The strip club is the turning point, she's met with an emotional, respectful and supportive guy who is willing to take a bottle to the head for her honour. This throws her plan into disarray and you see the visual metaphor of hearts in her eyes. At the halloween party she makes another play. The day after when Tremolo tries to spoon her, she's trying to keep him at arms distance emotionally, she's realised he is probably catching feelings as is she, this isn't the plan, before making her 4th play at "rolling"
After class, she kisses Tremolo, at this point the only time she has kissed him in a non sexual way is sucking on his tongue which she clearly stated was to make people uncomfortable, such as doing it in front of Sarah (who would not care less realistically), this time in a quiet hallway, she slips up and gives him a genuine kiss.
At the barbecue, she is called out, people are noticing she's catching feelings, she again tries to shut down any emotional talk, before being honest about why she can't let emotions get involved and asks Tremolo to keep her at arms length, before blowing him, trying to reinforce the idea of it just being a sexual and status thing. Before then deciding to stay in his tent and spooning
On the surface it seems like she is blowing hot and cold with Tremolo, but i think that is genuinely what's going on, her heart wants him, but he doesn't fit into the plan. I think the camping was her giving into her heart and her parts of episode 11 will focus more on that. Even if she tells herself that it won't affect her work, i think it will
For me, the rolling was her basically trying to "pre-order" Tremolo, she wants people to think they're together so they leave him alone, so when he fits into the plan, she can have him properly. But she didn't expect to catch feelings as quick as she has, and each interaction is making he fall more