My suggestion would be try and come up with a plan and agreement with your neighboring farmers/landowners to form an effective cull plan of troublesome foxes over a larger area. You may well find that somebody is already culling all the wrong animals and therefore creating a problem or perhaps you just have a too higher population for the natural food sources. A good number of foxes will live on very little and are experts at finding their own food, however in some situations (high population/ close to towns/ tips/ large industrial areas) unessential killing of the wrong species can be learnt behavior.
In some places where a healthy population has been established,good animal husbandry has been adhered to and on the whole most of the farming year passes without any clashes we have used feeding methods. For the critical weeks where a vixen need to feed her young and young lambs seem to be presented to her as if by magic, creating another food source will often provide her with all that she requires. We ONLY feed natural food that the vixen could catch for herself if she wasn't tempted by an easier option.
On a similar vein i fully understand that loosing lambs is gut wrenching problem, but from the months of March through to June a vixen is trying to feed her young, and without her they will simply starve.
I attend a lot of lambing call and see many many foxes among lambs and ewes but a lamb killing fox is generally very obvious in its behavior. As are some lamb killing badgers which is far more common than some would have you believe.
