We will have to disagree on that then

I can only comment from my knowledge and try and be helpful. After 15 years of being a professional rural pest controller (90% of paid work being foxes) i have a fairly good idea of their habits and control methods, also a fairly good idea of the majority of other peoples control methods.
Most actual lamb killing is done just before light or just as it gets dark as this is when lambs are slowing and settling or getting up. Unless they lambs are being born outside but most on here seem not to be.
A fox in among lambs/sheep is very common and causes very little disturbance unless specifically targeting lambs. most just clean up afterbirth or more often milk rich shite without being a problem.
Nowadays most people who lamp with a rifle drive most of their permission and therefore create disturbance and push about settled sheep/lambs.
Effective pest control is as much about observation as anything else.
Snaring can be a very effective control method but less people would volunteer to snare for free, it involves more skill and again it is non targeting.