Perhaps I'm missing things coming from a different background, but as far as I remember from my high school, our teachers had no trouble addressing each other by their first names in front of us, although they used honorific + surname when addressing us and talking about each other — which seems to be the way things are done at Hogwarts too. I seem to recall both Dumbledore and McGonagall addressing Trelawney as "Sybill" in front of the students, despite carefully referring to her as "Professor Trelawney". The one exception is Hagrid, whom nobody anywhere calls "Rubeus", not even Olympe Maxime, but again, I have at least one good friend who is better known by his surname than by his first name. (Again, there's another example, though in the Ministry rather than at Hogwarts: Nymphadora Tonks.) That being the case, Lupin is simply doing things the way they are usually done. His first use of "Severus" is therefore intended to show Harry, and perhaps to show Snape as well, that he and Snape are on the same team now and personal dislike should not be an issue between fellow-professionals. It is both unprofessional and unfriendly on Snape's part to address Lupin by surname alone as if he were a student. And while Lupin clearly deliberately ignores this signal, I'm not at all sure he's wrong to refuse to descend to Snape's level.