Yes, Lúthien's initial opinion of Celegorm is something I am curious about!I wonder if the initial interactions between Celegorm and Luthien could be genuinely friendly. He might feel like he is understood by her. She appreciates his love of living things (which is something she loves about Beren). From his perspective even if she remains in love with Beren for now, he is mortal and so Celegorm might reckon he has a chance once Beren has died even if of old age - and he must think that Beren will not survive captivity at that point anyway. She’s not necessarily going to be getting the full picture of C&C‘s usurping of the rule of Nargothrond.
On the other hand, Luthien would be well aware of the Feanorian involvement in the kin slaying and their status as persona non grata in Doriath so that would counter any initial friendliness at the beginning. Not sure how to get around that, unless Luthien is playing a peacemaker role, or can see how C&C might help her cause (Which I assume at this point is simply to rescue Beren and not to get a Silmaril).
Obviously, we know that he is enamored with her beauty from the moment he first sees her. So, he likely acts like an idiot . Watching guys trip over themselves in the presence of a beautiful woman is amusing, but I have to imagine Lúthien is used to this type of behavior, and likely handles the situation gracefully. But that isn't likely to make her think well of him. And as soon as they exchange names, the kinslaying would come between them. So...does he conceal his name or identity? Do they tell her they are 'elves of Nargothrond' and not reveal that they are Sons of Fëanor? That level of deceit up front would definitely put a damper on any possible good will she has towards him, and then the imprisonment situation would not help!
One of the only places that Beren and Celegorm's characters overlap is in their love of animals. And, yes, she must know that about Celegorm, because she uses that to help persuade Huan of how worthy Beren is.
I doubt Lúthien has any interest in Celegorm, even of the 'nascent friendship' variety. It's possible that she sees him as a potential ally in her quest to rescue Beren at first, but quickly realizes that his dog is the true ally here. Rather, the audience should see Celegorm as a beautiful elven lord who 'looks right' with Lúthien in a way that Beren doesn't...but is arrogant enough that literally no one is rooting for them to get together. People can feel sympathetic for poor jilted Daeron...but no one is going to think that Celegorm didn't fully deserve to have his dog stolen.
I am not suggesting we portray Celegorm as the unwanted love interest in Titanic, where he kicks old ladies off life boats to prove what a jerk he is. Celegorm simply behaving in a way that makes it clear that whatever 'love' he has for Lúthien is selfish and controlling would certainly be sufficient to demonstrate how unworthy he is of her affection.