No, we don't generally recommend using an invisible
fence with a LGD. LGDs are self thinkers who will respond to threats even if means taking a hit from a collar. Invisible
fence can be useful to reinforce a visual fence where the dog is digging out or climbing over. The other problem with invisible fence is that predators, children or other people, or wandering dogs can enter your LGDs area. Again, your dog may view them as a threat.
Some folks in more remote areas do have success with powerful radio fences but these tend to be more range situations.