Saute lamb and onion in a large skillet over medium high heat for 4 to 5 minutes; when lightly browned, stir in tomatoes, beans and mushrooms. Add 1/2 of the salsa and cook all together until heated through.
Spoon mixture onto tortillas, dividing evenly; roll up tortillas and place in a lightly greased 9x13 inch baking dish. Spread remaining salsa over the top and sprinkle with cheese.
Bake at 350 degrees F (175 degrees C) for 30 minutes, or until cheese is melted and bubbly.