Yer. . . . we've had a few problems here. Had a few sheep killed.
There is a real fashion for lurchers these days, I see a lot of non working dogs in pet homes. . . and by and large it's good, people rescuing dogs. In the working lurcher world there are a lot of dickheads who have them as a fashion accessory to make them look 'well hard'. Unfortunataly both sets of people, who end up with the dogs for the wrong reason, don't understand the basics of training and dog handling.
With a high drive dog like a lurcher can often be, that will end in tears. . . . or dead / maimed stock.
Having said that its true of most dog breeds. . . . we've also lost sheep locally to other breeds, in fact more so than running dogs, mostly pet dog owners with say a boxer, that never thought about stock breaking!
And like you say there are ways, if the dog is older, or you don't have the facility to install the training, to avoid hassle. . . by keeping your eyes open and using common sense. A lead is also a great tool!
With my lot, stock breaking is one of my main priorities with a puppy, that, and recall. If I can take them places, and they don't chase stock and come back when called. . . thats a great start! I also only take the dogs out 1:1 until about 7 months old, working on building a very strong bond, so i'm the most interesting thing around. As they get older I integrate them into the pack. Then through their working life they do different tasks, sometimes together, sometimes apart (i.e shooting over the spaniel, lambing with the lurcher, ferreting with the whippet or hunting the whippet, lurcher and terriers in a pack)
I can take my lot out all together, and they will do as I say, ignore sheep, cows, horses, chickens etc. However, if you are a rabbit. . . . or most other edible game. . . . then watch out haha. And I pity the fox that tries to get my chickens. . . .
I can't think of a better way to spend my time than in the woods, with my dogs, watching them do what is natural to them. And if they feed the family and themselves in the process. . . . that's a bonus!