This tangy relish can also be tossed with steaks, grilled pork, or grilled chicken.
Make relish: In a large mixing bowl, combine onion and lime juice. Season with salt and pepper. Cover tightly; set aside to marinate, about 1 hour or up to overnight.
Make burgers: In a mixing bowl, gently combine ground beef and Worcestershire sauce. Season with salt and pepper. Divide into 4 equal-size patties.
Heat a large nonstick skillet with a tight-fitting lid over medium-high, until water droplets sizzle. Add patties; cover. Cook until golden brown, turning once, 6 to 8 minutes total. Place each patty on a slice of toast, and garnish with onion relish.