Add black beans, eggs, lemon juice and spices to a large bowl. Use a large fork to mash everything together—no need to blend it completely. Some larger pieces of black bean are ideal. Fold in bread crumbs, rice and lentils until it all comes together. If mixture seems a bit dry, drizzle in a bit of olive oil until everything is evenly moist.
Using a 1/3 cup measure, pack it tightly and portion out mixture. Release into your hands and shape into 4 equally sized patties about the same size as buns. Brush each burger lightly with olive oil.
Heat a non-stick skillet over medium heat. When hot, cook about 4 minutes per side until burgers are browned and heated through.
Remove burgers and toast buns lightly in the hot pan. Serve on toasted buns with lettuce, mayo, pickles and red onion.
Note: ¼ cup lentils can be substituted for ¼ cup leftover rice or additional black bean.