In small bowl, place onion slices, lemon juice, sugar, and 1/4 tsp salt. With your hands, massage onions until tender and pink, about 2 minutes. Chill until ready to use.
In large bowl, gently combine beef, 1/4 tsp salt, cumin, and black pepper. Shape into 4 patties.
Build medium-hot fire in charcoal grill or heat gas grill to medium-high and grease grill grate.
Grill burgers for 3 to 4 minutes on each side, until internal temperature is 165 F. Re-move burgers from grill, let rest for 5 minutes, and then slice into quarters.
Divide salad greens among 4 serving plates and top with burger chunks, tomato, onion, pickles, and cheese.
Stir together mayonnaise, vinegar, tomato paste, garlic, and paprika. Drizzle dressing evenly over salads.