Place lima beans and 2 tablespoons olive oil in a food processor and pulse until lima beans are finely chopped but still have a little form. Place in a large bowl.
Add red pepper, corn, cheese, 1 cup of panko crumbs, egg, and salt. Mix well and shape into 5 patties. Coat patties with remaining panko crumbs and place on a plate. Cover with plastic wrap and refrigerate for 30 minutes.
After 30 minutes, heat 2 tablespoons olive oil in a large nonstick skillet over medium heat. Add burgers and cook until golden brown and crispy, about 4 to 5 minutes per side. Add more olive oil if needed. Drain on paper towels.
Wipe skillet clean, add 1 tablespoon of oil and cook onion slices 1 to 2 minutes per side.
To make Basil Mayonnaise, mix all ingredients in a bowl.
Spread Basil Mayonnaise on bottom of buns and top with burgers, bacon, onion, and tomato.