Combine beer and steak sauce in 1-cup glass measure. Cover and microwave on HIGH 1 to 1-1/2 minutes or until bubbly.
Lightly shape ground beef into four 3/4-inch thick patties. Place patties in center of grid over medium-ash-covered coals; arrange onion slices around patties. Grill, uncovered, 13 to 15 minutes to 160°F internal temperature. Season with salt after turning.
About 2 minutes before patties are done, brush generously with sauce; top with cheese.
Serve burgers and onions in rolls with lettuce and sauce.
