I'm not sure im the best person to advise so maybe someone with more experience might be able to explain possible reasons, all i can think of doing is eliminating certain things. How long have you had him and has he always been like this? Was he recently bonded with Lily or recently been neutered? What was his past like if he had one, bad that is? Also what is the relationship like with Lily, is she the bossy dominant one for instance? It could just be a personality thing and he's just a more nervous bun? It could also be a certain smell, I'm not sure if buns, like humans, react to smells in different ways, maybe he dislikes the smell of something that Lily is ok with?
Sorry for the questions but it might help to work out what it might be.