If it has oil holes, there are two of them located on the topside of the motor housing. One would be on the very top edge and the other on the bottom edge. Some of the LG pumps have sealed bearings and enclosed motors and cannot be oiled. They all run very hoty compared to many other brands. I have had several of these pumps go bad on me. The heat is probably a contributing factor. The sealed bearings develop leaks, the lube runs out and the motors sieze up with no way to oil them. If your pump does not have oil holes and the motor doesnt spin, the bearings have most likely leaked their lube and it is shot. You can send it back to LG for repair/replacement but you'd probably be better off buying a new one for what it will likely cost you. You can also buy a replacement motor which will save you a few bucks over a replacing the entire pump. I am not making any claims regarding the fitness of Little Giant pumps in general, I am just giving my experience with the LG pumps that I have owned over the past 20 years.
I have just had too many LG's over the years that have died because of the same reason. I wont buy another LG unless it has the oil holes and can be oiled. In fact, I recently switched out my 2 main pumps which were LG's to Blueline pumps. I cant comment on their long term durability but they cost less, run signifigantly quieter and much cooler as well. So far, I have no complaints and my chiller runs for 10 minutes less each cycle since switching pumps.