I think you need to think this through macvity and make sure you do everything legally. I'm not sure if you're in Eire or NI, the law may be different between the two.
Firstly, for all of us as livestock keepers, our initial reaction when our animals are attacked is fury and the need to take revenge. We must not do that. Our comments here have been made without having much information.
#how well is your land fenced? You can't reasonably expect predators to stay off your land if you haven't done your best to protect your animals by good fencing.
#Are you sure this is a dog attack? Could it be a badger or a fox?
#if you are sure it's dogs, is it definitely your neighbour's dogs, or are you assuming that? You would have to see the attack in progress, and photographic proof would be good. Seeing blood on the dogs muzzles would also be very suggestive that it was them. At this stage you should report the attack to your police force. If livestock crime is taken seriously in your district then they can compare saliva DNA from the dogs with that from your lambs and that would constitute proof in the eyes of the law. It would then be up to the law to deal with the problem. At this stage ask them what your rights are. Please please don't make threats against anyone.
#You should also approach your neighbour again, and let him know that you have reported the situation to the police. Don't be aggressive, and if he becomes aggressive then walk away.
#If none of these measures work, then it may be that you will need to deal with the dogs yourself. As Sally says, if you intend to shoot the dogs, you must do so during an attack, if that is the only way to deal with them ie you or your neighbour is unable to recall them. You must have a clear field of fire, and this is not possible if you have close neighbours, or walkers paths nearby. If you do shoot and kill the dogs then you must report it to the police. You must make sure you are not committing a gun crime yourself, or any crime.