Just read your post - yeah, I don't think I'd have him hunting unless he needed to do so. Owlin can certainly hunt but even then would be inclined to cook their food. And he eats a lot of what other humanoids would eat.
But . . . I think he would tend to sleep in a tree. They usually have houses high in the trees and while travelling he owuldn't have the house part, but would still prefer to be off the ground when possible. At least that is how I'd do it. Remember, there is no info on this so I'm making it all up as we go.
A for the post - in any fight Azax's preferred strategy would be to take to the air. He has an advantage there and can get out of range of enemy melee weapons. I'm asuming an owl can take to the air in a forest, but how high could he get and see the lizardfolk? What limits do you want to put on him in this setting?