Cook ground beef and half of the diced onion in a 3 to 4 quart saucepan over medium-high heat until beef is no longer pink, then drain excess liquid.
Reduce heat to medium-low and add ketchup, pickle relish, and mustard; simmer for 3 to 4 minutes.
Remove from heat, stir in shredded cheddar cheese and black pepper until well combined.
Melt cubed Velveeta cheese in microwave-safe bowl using 45-second intervals, stirring until smooth.
Warm tortillas in a microwave-safe tortilla warmer for 45 seconds.
Spread ½ cup beef mixture over a 4x2 inch section of each tortilla.
Top beef with 2 teaspoons of remaining diced onion.
Add 2 tablespoons melted Velveeta, shredded lettuce, and chopped tomatoes on top.
Fold sides of the tortilla over the filling, then fold bottom over the sides and roll tightly to form burrito.
Serve immediately.