Don't have any LGD's of my own but have vicarious experience from friends. I leased part of our farm (50 acres) to a friend who placed a flock of 30 sheep and 1 guard dog on the farm. That guard dog (1 yr old) guarded not only her flock but our flock and the neighbors horses. The dog would jump our 5 ft smooth wire electric fence to get out of the alloted pasture and make her rounds to our pasture, the neighbors' pastures. The guard dog was very friendly with people, but we could not keep her confined in the pasture on our farm. Ended up chaining her up with her flock. Needless to say, the guard dog became frantic and was difficult to manage. The friend had to give her to ranchers that grazed thousand acres of BLM and were far from other flocks or farms.
This guard dog also would not tolerate our Border collie gathering sheep (hers OR ours) to herd them into shelter at night. From numerous accounts, LGD's are dangerous to all other dogs. For example, we know of another LGD which was guarding her flock and unprovoked attacked a visitor's Border Collie and tore the Border Collie's chest out. Almost lost that dog.
Another friend had an LGD for 3 months. She could not keep that dog on her property. It jumped fences as well and adopted the flocks in the entire area.
I train my Border Collie in the desert on my own flock but cannot go there if the local ranchers are running their sheep in the area with guard dogs. The guard dogs will attack my dog and adopt my flock even though they do not know my sheep. That is their job and I respect the work ethic.
Don't get me wrong, I respect and approve of using guard dogs. Better that than loosing stock or killing predators but they can be a management problem in cases where they are located in proximity to other flocks or encounter other dogs.
FYI, border collies cannot tolerate ivomec. Not an old wives tale.