Yes, they exist. When I grew up on the north shore of Chicago, there was (still is) a local chain of restaurants called "Hackney's". Hackney's was/is a nice place. Dark rooms, tablecloths, a bit fancy. But their fry station....oh la la. They deep fried burgers in lard. Also onion strings (which I sorely miss from Olives...but that's another thread). Hackney's no longer fries their burgers. *sigh*
Watch City Brewing in Waltham now serves deep fried burgers. They batter dip theirs before frying (not quite right, in my book) and they're OK. Would be better in lard and without batter.
Anyone know where else one can find deep find burgers (with or without batter)?
PS. My mom claims that North Shore Congregation Israel (also near Chicago) used to have a cook who everyone loved because his burgers were soooooo good. Guess what his secret was? When they found out he was using lard (this might have been OK as the Congregation was Reform), the cook got the boot.