1. Divide beef into 2 equal portions, shaping each into a 1/2-inch-thick patty.
2. Heat oil in a nonstick skillet over medium heat. Place patties in pan; cook 6 minutes each side or until a meat thermometer inserted into middle of burger reads 160°.
3. Combine green beans, white beans, kidney beans, carrot, bell pepper, and vinaigrette in a bowl; toss gently.
4. On the bottom of each bun, place a few lettuce leaves and 2 slices tomato; top with burger and other half of bun. Serve bean salad alongside burgers.