Hi Whitehood, sorry to hear that Lucky has an infection.
My bun Bunny has snuffles too. Unfortunately, his is quite ingrained and we have not been able to eliminate it from him, but as he is stable with it, on my vet's advice we do not treat unless it worsens.
I hope that someone with a bit more knowledge on this can advise you properly, as I have to admit that I have heard/read varying opinions on this. Some people say that it is highly contagious, but others say the bacteria is in all buns, but some are more susceptible to the symptoms (eg if their immune systems is compromised, or due to stress etc).
I ALWAYS work with my vet with Bunny's snuffles, and go by his advice. I would be really interested to read other people's advice to you on this, though, as there will be people on RU who have dealt with snuffles a lot and have a better idea about it.
ETA: I should have said that Bunny's snuffles has been around for a long while, and it is entirely probably that with Lucky, as you have just caught it, the symptoms can be nicely controlled by the abx. I just realised my post sounded a bit doom and gloom, and I don't think this reflects Lucky's situation at all! Do you have treatment for Lucky from your vet?