Lum's was a chain noted for their hot dogs cooked in beer and for their "Ollieburgers".

Lum's was founded in Miami Beach in 1956 by Cliff Perlman and his brother Stuart. Within a couple of years Lum's had become a 389-unit franchise chain that spanned Canada, Puerto Rico, and 29 American states. In 1971, the Perlmans sold the company to John Brown of Kentucky Fried Chicken.

I have had no luck finding a recipe for the "Lumburgers" that preceded "Ollieburgers" at Lum's.

What Kind of Hot Dogs Did Lum's Use?

You Can Buy Lum's Ollieburger Spices Here

Ollieburgers & Beer Hot Dogs
Lum's & Ollie's Fries
More Great info on Lum's Recipes
Another Ollieburger Clone

There's a "from scratch" recipe here, however, it is admittedly a copycat: Ollieburgers

You can buy Ollieburger Spices here: Ollieburger Spices

Your best bet for an Olliburger is to use those spices and follow this recipe: Ollieburger Recipe
There is a lum's blog at : Lum's Recipes

Lum's is Back! A Lum's has opened at Lum's, 717 Fall River Ave in Seekonk, MA
The website says they have the original Lum's recipes.

No luck:

chili sauce for chili dogs
Lumburgers
Lum's Roast Beef