LG has a updated universal compressor to replace almost every linear compressor. Look up the part number by using the model number of the fridge not the numbers on the compressor.
It requires the mainboard to have a software update using a special jig.
I would suggest you do not make the repair to this fridge as there are other problems when these compressors fail that cause the condenser and cap tubing to clog with debris. Also there may have been a leak in the evaporator aluminum tubing that allowed air into the system causing the oil to gel up like wax.
I would suggest shopping for a new fridge to save yourself time money and future frustrations trying to fix this LG Kenmore.