Preheat the oven to 400 degrees F.
Pulse the chick peas, onion, garlic, cumin, 1 teaspoon salt, and 1/2 teaspoon pepper in a food processor until finely chopped. Sprinkle with the flour, baking powder, then pulse until just combined. Transfer to a medium mixing bowl and add the sausage, stirring together with your hands. Cover and move to the refrigerator to chill for 30 minutes.
Once chilled, divide the mixture into tablespoons, rolling into 1-inch sized balls with wet hands. Heat the olive oil in a large pan over medium heat. In two batches, add the falafel balls and cook until lightly browned, about a minute and a half per side. Transfer to a baking sheet and bake in the oven until cooked through, about 10 minutes.
Whisk together the yoghurt, lime juice, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Divide the lettuce between 4 serving plates, then drizzle with some of yogurt sauce. Divide falafel between plates and serve with hot sauce.