Rinse and drain the lentils. In a medium saucepan, bring them to a boil in 3 cups water. Reduce the heat and simmer, partially covered, until the lentils are tender, about 20 minutes. Drain and set aside.
Meanwhile, in another saucepan, bring 3 cups water to a boil. Add the potato and cook until tender, about 10 minutes. Drain and cool in a small bowl.
In a medium bowl, whisk together the tomato paste and egg until smooth. Mash the potato, then add it in, along with 2 cups of the lentils (use the rest in a salad or dip), the zucchini, garlic, green onions, and herbs. Season with salt and pepper and gently stir to combine. Place the mixture in a food processor and pulse until blended but chunky. Return the mixture to the mixing bowl and fold in the bread crumbs.
Divide the mixture into 8 equal portions. Shape each into a patty, dredge it with flour, and place on a plate. Refrigerate the patties for 30 minutes.
In a large skillet over medium heat, warm 1 tablespoon vegetable oil. Add 2 or 3 lentil patties, and cook until browned and warmed through, about 3 to 4 minutes per side. Repeat with the remaining patties, adding oil as needed. Serve the burgers on buns, with lettuce, cucumber slices, and other toppings.