No idea. That's why I asked if you have calipers. With calipers you can measure the thread diameter and thread pitch to find out what size it is. Otherwise, you could use a thread gage to get the pitch.
Do you have a tape measure? Hold it up next to the threads and get me a pic.
Home Depot will possibly have them, but if you have a locally owned little hardware store around, or an Ace Hardware, they will likely have them in bulk and you can just buy whatever quantity you need.
I would nut use a serrated lock nut there. Get nylon locknuts or nyloc nuts as they are also...
That type of nut with the serrated bottom is designed to be used withoit a washer under it. A nylon locknut would be better with the washer on there. You can find them in hardware stores.