Not the same person as
>>2, but I guess having more opinions is better right? Not a theater writer, but I'm a fanficiton writer (oof, ik) who also struggles with dialogue sometimes, so I thought I'd add my two cents.
I think most people in a situation like Luna's would just try to avoid meeting irl. They probably wouldn't say what they're afraid of straight-forwardly unless they were really backed into a corner about it.
It really depends on Luna's personality though, and what kind of friendship she has with Liam. Do they banter and poke fun at each other a lot? Can they usually be serious and heartfelt with each other, or do they tend to inject those sorts of conversations with humor? Also, how corny are they as people in general? Are they romantics or do they cringe & have a hard time with affection? All of this & probably more things factor into how you should write their dialogue. (You don't have to answer all these questions for me lol, unless you want very specific advice, but hopefully it can help point you in some direction? Idk)
For example– I really hate sounding mushy, and I text pretty closely to how I speak in real life, which is a loooot more casual than my writing tone here. Instead of texting "I'm afraid that you won't like me as much in real life. I'm not as funny or smart or pretty" I would text something way more stupid-sounding like "lmao no don't even start, i'm like an actual goblin irl". Is Luna also the type to resort to self-deprecating jokes?
I'm not sure how you're planning to have their dialogue be performed either. Is there meant to be a visual aid that will show the audience exactly what is being typed into the chatroom, or is every message being read aloud by the characters that send them? Because that would change how you write the dialogue too. (Texts written like mine would Not sound good read aloud. lol.)
I hope this helped at all, I know I didn't really give you a straight answer. Good luck with writing :)