How to Find a Model Number
If you order the entire drum assembly, the spider part comes already attached. It's also covered under their part warranty.
Call LG and tell them that it's your own washer and you want to repair it yourself. Give them the model and serial number and your information. The warranty does not specifically say that you have to have an authorized servicer fix it. It just the part is covered for certain period of time and you should be able to get the part for free under that warranty.