You're right, we're not told which curse Bellatrix used on Sirius. I hadn't noticed that. I had just assumed that she had spoken the Avada Kedavra curse. We're also not told what colour came from her wand. The spell before the one that hit Sirius in the chest the colour was red, which we know is not the colour of the Avada Kedavra curse since it's green.

But Lupin seemed to reckon Sirius was gone and we'd expect Lupin to be as devastated as Harry over the loss of Sirius - they were mates after-all.