Yes, they do, but it’s mostly between-the-lines ;A;

[I’ll warm your cold blood by DrKav]

You’d think, for one of the fandom’s main ships, there would be more of it explicitly canon. There just isn’t, sadly. But Lestat pines for Louis QUITE ALOT. In the immortal words of @hyperbeeb, “Now matter how hard you ship Louis and Lestat you will never ship Louis and Lestat as hard as Lestat does.” [X]

Part of why it’s such a tough ship is that AR just does not let us have much in terms of fluff of them! It mostly happens off-screen. Which is where fanfic steps in to satisfy that need ;]