Looks like a barrel plug. These are very common and finding s as replacement should be easy. On the underside of the lamp there will be writing that says what the electricity requirements are. e.g. 12V—-400mA Look up a replacement using those numbers.

Food Theory did an episode that covers exactly this.

TL:DW McDonalds owns the land and the franchise owner pays rent.

I wish I could fail upwards like that.