Make the Falafel Burger Patties: Transfer the lentil falafel mixture to the bowl of a food processor. To the lentil mixture, add the onion, egg, panko breadcrumbs through salt and pepper.
Form Patties and Cook: Shape the mixture into four 4- to 4½-inch patties, each about ½ inch thick. Heat a large frying pan or skillet over medium heat.
Make the Sauce and Serve: To a small bowl, add the feta cheese, then use a fork to crumble it. Stir in the yogurt and mint, and add a touch of lemon juice if desired.