They seem to be okay. There are two cats, both just keep “casually” strolling past the laundry room where the cage is and shooting furtive glances in his direction. When he’s out on the floor they’ll keep creeping up, wide-eyed to touch noses with the bunny then hurrying off to consider the situation from the other room. Both are 100% indoor cats and have never seen a rabbit before. The bun appears to have no fear of them whatsoever, and also doesn’t appear unduly concerned about the 120 pound dog who is extremely thrilled about this new development. Interestingly, it seems that having zero context re: predators shifts his attitude to neutral about pretty much everything. I’m really amazed at how quickly he’s adjusting and how confident he seems. Poe is a “retired” lab animal too, and it took him three days of practically being comatose to absorb it all. Arthur is a bit skittish here and there, but he’s taking it all in stride far better than the cat did.
By the way, anyone have any good bunny name suggestions? Arthur doesn’t seem right to either of us. Harvey? Spike? Basil? Reader? Ozwald? NajaHusband proposes we call him “Killer” and put a grenade on top of the cage with an “in case of escape…” sign. 
This made me recall the conversation recently with our vet. He was a bit amazed that our beagle (moreso than our golden retriever) got along with the rabbits. It is pretty much that anything inside the house is accepted as “family” anything outside the house is “fair game”.
Congrats on your new bunny! We’ve had several bunnies over the years and now have Val, who is a brown lop and looks exactly like a groundhog (except for her long ears).
I think there’s been a lot of great info already covered in this thread, so I won’t repeat it, but I did want to say one thing. Get a good vet who knows bunnies. Not all vets are familiar with bunnies, and something that’s okay for a cat or dog can be deadly for a rabbit. This is especially important if your bunnie was a former lab rabbit, as was one of our previous rabbits, Nikki. Nikki developed a huge tumor beind her left eye and had to be put to sleep. We believe this was because of her time spent as a lab rabbit–the vet said he’d never seen anything like that before. Also, when rabbits get sick, they “crash”. They’ll be fine one moment, then literally get deathly ill the next. We lost our favorite bunny, Bun, when he got an intestional blockage. Even though he was on an IV (intestional surgery would likely have killed him), and seemed to be coming along, a short time later he went from perfectly fine one morning, to deathly ill that evening, and died before we could get him back to the vets.
Now for the good news…Rabbits, like cats and dogs, have amazing personalities as you’ve probably already discovered. Val comes when called (and goes to her crate upon “Val, crate” command), loves to be petted and brushed, and completely freaks out my cat, Ailey (who is deathly afraid of her, even though he’s bigger and heavier). We keep her (and have all the other bunnies) in the diningroom pass through to the kitchen that gets a lot of foot traffic and since it’s right outside of the kitchen, gets a lot of “human noise”. (We adopted her from a local shelter and she was skittish when we got her. Not now!) Val is fairly large (about 12-14 lbs.), but we still hold her, being careful of her hind feet/legs (which are HUGE) and keep her well supported. (It’s necessary to hold her when we clip nails, or wash her butt–she’s often large to often properly clean herself.–I feel it’s necessary for her to understand that holding isn’t “punishment”, but can also be pleasurable, which is why we hold her with scratches and petting as well.)
Enjoy your bunny!
Luckily, our personal vet is also the vet that oversees the lab animal facility, so not only is he familiar with bunnies, he’s familiar with Arthur’s lab history, too.
I was surprised to hear all the “anti-holding” talk, I guess I just never realized that people don’t generally hold their rabbits. I used to manage a pet store. We never bought baby rabbits, but the local shelter would bring us rabbits to socialize and place, and we’d pick them up, handle them, pet them, and hold them all the time. I suppose it does make sense that it would be sort of antithetical to their nature, though.
I’ve two tricolored overlords in the house. I don’t think I wanna try and test this in-house bun theory. Poor bun.