Add beef and onion to a large skillet and heat over medium high, stirring frequently until beef is browned and onions are translucent. Drain grease and return to pan. Season beef with a pinch of salt and pepper.
In a separate bowl, whisk together mayonnaise, french dressing, relish, vinegar, onion powder, garlic powder and paprika. Mix well. Add 1 cup of mixture to the beef and mix well, heating over medium heat, stirring frequently until hot, about 2-3 minutes. Remove from heat.
With reserved big mac sauce, spread onto the bottom of each bun. Top with beef mixture, a slice of cheese and shredded lettuce. Add top bun and serve.