Combine lentils, water, and bay leaf in a medium saucepan. Bring to a boil, then reduce heat and simmer, uncovered, for 20-30 minutes. Add more water as needed to keep the lentils just barely covered. The lentils are done when they are tender. Drain any excess water and season with salt.
In a food processor, process walnuts and sunflower seeds until finely chopped. Transfer to a large mixing bowl and set aside.
In the same food processor, process the carrots until finely chopped. Add the carrots to the walnut mixture and do the same with the onion.
With a wooden spoon or spatula, mix together walnuts, sunflower seeds, carrot, onion, garlic, breadcrumbs, thyme, oregano, ½ teaspoon salt, and cooked lentils.
In a separate small bowl, stir together egg, tomato paste, and worcestershire sauce. Add to the lentil mixture and stir to combine. Add the flour and stir until just incorporated.
Cover the mixture and refrigerate 30 minutes or up to overnight. Using your hands, form into six equal patties. I like to make the patties thinner rather than tall so they cook evenly throughout.
Heat 1 tablespoon olive oil in a large skillet over medium heat. Working in batches as necessary so as not to overcrowd the pan, cook the patties in the hot oil for 8-10 minutes, flipping once, until lightly browned and heated through.
Serve lentil burgers with lettuce, tomato, and onion slices on hamburger buns. Top with barbecue sauce, ketchup and mustard, or whatever your favorite burger toppings are!