Combine the meat, fat, salt, and pepper by hand and form into four balls, then make a little dip in the middle of each for the filling.
Spoon a tablespoon-full of the guac into the center of the patties. Place the remaining two patties on top and pinch the sides closed. Arrange on a foil-lined baking sheet.
Scrape the gills out of the mushrooms and brush the top and bottom of each cap with coconut oil. Sprinkle with salt, then arrange bottom-up on the baking sheet.
Bake 10 minutes, then flip over the mushrooms and bake an additional 10 minutes.
Serve the burgers sandwiched between two portobello mushrooms with the lettuce and any extra guac or additional toppings.