Preheat grill over medium high heat.
In a medium bowl, combine sirloin, onion, garlic, salt, pepper, and Worcestershire. Divide into 4 equal pieces and form into patties.
Drizzle olive oil in a large skillet over medium high heat. Add the sliced mushrooms and cook, stirring occasionally, until liquid from mushrooms evaporates and mushrooms darken, about 8 minutes. Stir in garlic and shallot and cook until just fragrant, about 1 minute. Stir in tomato paste until it browns, about 1 minute. Remove pan from heat and stir in Marsala.
Return pan to heat and increase to high. Simmer, stirring often, until the liquid reduces to 1 1/4 cup and thickens, about 5 minutes. Whisk in lemon juice and butter until melted.
Grill the patties on preheated grill until cooked through, 3-5 minutes per side. During the last 2 minutes of cooking, place Provolone slices over each patty. If desired, place burger buns, cut side down, on grill to toast. Place burgers on toasted buns and top with mushroom marsala sauce.