On Lily path, she is already in love, she's just fighting so hard to keep it under control, so she doesn't have to give up stripping. She comes up with this rolling bullshit, so she can justify it's not a relationship (which it actually is), and not lose the money she needs for B&R.
And imo, she's a lot more open about who she is, what she's doing, what her feelings are, and future plans than Quinn is.
And of course, a much better girl to take home.
Tremolo: Hey Dad, this is my girlfriend Lily, she's stripping to pay her way through college.
Neil: That's honest work, I like people that work hard for their goals. What are you studying?
Lily: I'm going to work in Healthcare.
Neil: Wow, that's really admirable, and you'll come out debt free.
Tremolo: Hey Dad, this is my girlfriend Quinn, she's a drug dealer and runs a prostitution ring at B&R.
Neil: Twice a criminal, can't say I like that very much, but at least she's rich.
Tremolo: You'd think that wouldn't you, but no.
Quinn: I like broccoli.