For the burgers: Add the beans to a large bowl with the breadcrumbs, lemon juice, oregano, salt, pepper, garlic, eggs and onions. Mash with a fork or your hands until the mixture is homogeneous. Portion into 6 patties and refrigerate for 1 hour.
For the mayo: In a small bowl, mix the mayonnaise, oregano, pepper, salt, garlic and lemon juice.
Heat a medium pan over medium-high heat and add the olive oil. Cook the burgers until golden brown, 3 to 4 minutes per side. Place each burger on a bun, and top with lettuce, tomatoes, onions and some Greek mayo to serve.