So this is after only a month of introduction? I'd call that pretty remarkable.
We were adopted by a young, stray cat in mid-July and we're only up to 20 minutes under strict supervision with our 5 older (ages 10 to almost 15) English setters. Yes, we're being super cautious!
I would have to see the dog in action to know for sure what his intent was when he lunged but it
sounds like he wasn't out for blood, but just warning them off in both cases. Do your cats have safe places to run to where the dog can't get to him? Will they defend themselves (do they have their claws?) if attacked?
I think to be on the safe side, I'd still be separating them when they're unattended, but you're off to a great start! You can always feed the dog behind a closed door if you're worried about that aspect of it. (We feed all of our dogs in separate areas and the cat is kept away at dinner time.) The thing that would concern me most would be the couch incident, if it turns out that the pooch was guarding you as a resource--in that case, a little behavioral modification might be necessary to discourage it. But if it's only been the one incident in a month, and you aren't certain what cat/dog interaction precipitated it, it's just something to keep in the back of your mind. Be watchful, but don't worry too much till you know what's going on.