The hole on the base of your camera has a 1/4"-20 turn thread. That's sort of the default standard. Most tripod QR plates and whatnot have 1/4"-20 turn screws to fit into that hole. The bases of many tripods have a 3/8"-16 turn screw to attach to the tripod head.

The adapter you bought has a 3/8"-16 screw on top. You'll want something Like this to add to the screw on top of the kupo mount you bought. That will screw into the base of your LED lights (assuming they are 1/4-20, which seems likely).