The lines are tied directly to the Exploration Cartography information you have on the system you're in. If you have no info, and do not scan a system, there are no lines. They only appear once you've either scanned or purchased cartography info on that system.
This means there is already a "display lines=true" and "display lines=false" state built into the game, based on this cartography info.
It should not be very difficult at all to allow for the player to manually toggle this state either on or off, since the "on" or "off" states are already built into the game.
Please make this happen FD! Those lines are useful at times, but completely ruin the beauty of this incredible galaxy you've so painstakingly created. Please let us toggle them on or off with a key bind.