LGs are just that. They are and have been, bred for hundreds of years, to stay with the flock and protect it. There are also, many different breeds, of LGs.
They have been bred to think for themselves and most don't take easily to formal obedience training. They have a bit of a feral streak in them. They will take on anything, which they consider invading their property. That means domestic animals, which which they have not been brought up with, wild animals and even humans. The have a big bark and use it! So if neighbours are close, most are not suitable, since they do bark at night if they hear or see something. This is one of the reasons, we see so many in rescue. People get them in the city and soon have neighbour troubles. Our local GP rescue is always full. Texas GP rescues, have so many, they often ship them out here to our California rescues.
A note on rescues.
With so many losing their farms these days, there are some excellent true working dogs available. Most of the time, the rescues know which animals they have been brought up with. Don't expect such dogs to be your friend. They will likely be aloof and except for the usual care, prefer to stay out with the flock.
They are very territorial and with that, comes the problems that they often consider everything they can see, their territory. If (for example) a coyote enters the property or comes close to fencing, they will do anything to keep on chasing it. They will climb, jump or dig under fencing, to dispatch the invader.
Many LGs have for generations, not been used for their intended purpose, so have lost some of their previous instincts. It is still there, but not quite so much as those who have been bred purely as working dogs.
Many LG breeds have some major genetic problems. Unfortunately, not all those who breed for work, test their breeding stock. People who breed for the show ring, are more likely to have their stock tested, but they might not necessarily, be the type to do the job alone and left out.
A good LG breeder, will have tested his dogs for all the genetic problem known in that particular breed. His dogs will have lived with the flock from puppyhood.
Some LGs are or can be, very aggressive to all but the owner. Most would not be suitable to guard a flock and also take out in public on a trail ride. It would likely try to attack and even kill, loose dogs accompanying other dogs, he might meet along the trail. Remember, LGs consider everything their own territory.
Certainly there are other breeds, which might be able to handle home security and also go on trail rides. Irish Wolfhounds, Scottish Deerhounds and a few others might suit. IW's however, have many genetic problems such as heart disease, so the breeder would have to be carefully chosen. Also, being bred as a sight hound, they are more likely to take off when out and about. That would involve careful training and a very solid recall.
GP's seem to be a favourite guardian breed. I would not recommend a Causasian Ovcharka to anyone, not extremely knowledgeable with LG breeds. Beautiful dogs, but most are extremely aggressive and focused. Definitely not for the novice or faint of heart.
Anatolians can be a good choice. We have owned one. Not so much coat to deal with, as a GP for example. Escape artist supreme. She didn't jump fences or dig under, but learned when the electric gates opened, she could escape. The neighbour had a very old African Lion, down the road. He was in an enclosure and had been an old movie animal. He never bothered anyone, but our Anatolian always made a beeline for his property, to try to get him. We always knew where to find her!
I suggest a whole lot of homework about all LGs, before jumping in.
GOOD AND SOLID FENCING IS A MUST FOR ALL LG BREEDS. Everything they see, they consider their territory.
They do try to escape and wander, given the chance. We constantly find them loose out here in S. Cal., wandering through the desert and mountain areas.