Well, I guess everyone owning rabbits would be happy to keep the wild population at bay, in my first year with rabbits they killed 14 of my 15 buns by spreading Myxo.
A fence works for your vegetables, a double fence at least 1m apart should keep them from spreading desease easily. Also dogs with the right attitude would work. I'm not sure about cats, although some kill small rabbits that isn't in a way to defend your property.
Poaching and eating some didn't solve the problem either, but I moved to a valley where too much predators roam to allow any wild rabbits, on the other hand that causes some problems for my rabbits too...
About rabbit poop on the lawn: Just convince your friend it's perfect, organic fertilizer, a sign that everthing is ok in his garden, and that bunny berries are actually a blessing
, much better than putting up a fence or let out the dogs...
I'll never understand what's so great having a "perfect" lawn...