Brush the mushroom slices and swordfish steaks with olive oil and season with salt and pepper.
Combine the thyme leaves and lemon zest and sprinkle generously over the mushrooms and fish. Toast the bread slices until golden. Combine the mayonnaise and chili puree.
Wrap the fish with the thinly sliced bacon. Heat a skillet over high heat and add the mushroom slices. Cook the mushrooms until they begin to brown before turning and quickly cooking the other side. Remove the mushrooms and add the fish steaks to the pan. Cook the fish steaks for 2 to 3 minutes on each side.
Place a lettuce leaf on each piece of bread and top with a mushroom slice, then a fish steak and finally mushroom slice. Place a dollop of mayonnaise on top and serve.