The ice maker will not shut off on the LG refrigerator.

I can think of two possible problems. The ice has frozen together and will not allow the ice screw to push the ice out the dispenser. Or the motor for the ice screw is broken.
1. Shut off icemaker with lever at icemaker
2. Remove ice container (either throw away ice or save in another container).
3. Put back empty ice container.
4. Leave ice maker off for about an hour.
5. After an hour , check if motor is working by trying to dispense ice. You should not expect any ice but you should hear the motor /auger moving.
A) If you do not hear any thing , you need to get your motor replaced.
B) If you hear the motor , mostlikely you had an ice dam which prevented the ice dispense from working..You can turn you icemaker on.

unplug icemaker in and out

the icemaker arm on the L g are diferent dont try to pull up not a shut off arm this has a switch under side of ice maker if u kift up on the arm on this icemaker yo uwill need to buy a new icemaker and they arent cheap check for an ice jam between auger in icemaker if you havent pulled up on arm ive also seen the water fill tube to icemaker frozen

I'm having trouble identifying that model number, but I can give you the generic answer. On most icemakers the "shut off" is lifting the wire arm to the up position. It should lock in that position. Lifting the arm shuts it off in the same manner that it stops the ice maker when too many cubes are in the tray. I have seen some icemakers that actually have a swich on the front side of them. But, they are in an obvious position so I'm guessing you don't have that style.
Hope this helps

Appliance parts online

http://www.appliancepartspros.com/partsearch/

Second option - Go into the ice business

Pour about 1/2 cup of water into icemaker . If it dumps , replace the water valve . If doesn't dump , replace the icemaker . Also make sure the coils are clean of dust , lint , etc...

its the ice maker .water or condensation has built up in the ice maker modual and refroze upon turning unit back on.either get a new ice maker or uninstall the ice maker and let it dry for a few days and reinstall.but it could happen again that way.or maybe not.

there should be a saftey shut off bar or something in there to shut the ice maker down, look inside and see if there is a bar, or holes where a bar should be installed, if there is a bar, the the auto shut feature is not working you will need to replace it if thats the case, best of luck, hope that helped

hi. thanks for the question. is the arm on the ice maker in the up position. it could be stuck in the ice cubes. the arm has to he up to stop the process thanks the appliance doc.

You may have a problem with the computer control board in the ice maker.  Try this.  Turn off the icemaker for about 2 minutes.  
Turn on the ice maker and press the clear button.  Press and hold this button for 12 seconds to get it to force extract.  This will confirm that the motors will work and push the ice cubes out.  Afterwards, let it run by itself.  If it still doesn't make ice, you will need to replace the icemaker.