Part of Lavi is jealous over the good relationship that Kaworu has with Allen, it's almost like he's been nudged out of the spot he once claimed. And it kind of hurts to see how much Allen relies and confides in someone who's a stranger to their home. But...he can't really justify staying "upset" (only way I can explain it) at Kaworu, especially when he starts finding things out about the other and his world.

Lavi's curiosity rules out any other feelings he might have, negative wise. On the positive side of the spectrum Lavi finds Kaworu nice enough although it feels as if his inquiries about one's health or being alright is just pleasantries. Like...it's all shallow water and while it's water and life-giving it's not the substance that the deeper waters can provide? Like he's doing it for politeness.

And with that Lavi feels like he's facing himself almost. A heavy mask is on Kaworu's face, the real persona beneath it so deeply buried that it might not even be there anymore. Lavi's not curious enough nor attached enough to Kaworu at this time to want to try and find that person. But it might come.

As it stands right now he'll come to Kaworu's aid mostly because he means so much to Allen.