LG Refrigerator Informative - Ice Maker
You can go to Home depot and buy a plastic valve that will go on the water line for the Ice Maker.
The valve cost me $6.50 and it's works great.
It will take you less then 10 minutes to fix your problem. No tools needed, all you have to do is cut the line and put on each end of the valve.
Try it and you will thank me.