Place lentils in a container. Pour in enough water to cover and let soak, at least 30 minutes. Drain.
Combine drained lentils, 4 1/4 cups water, ground chicken, onion, green chile peppers, ginger-garlic paste, garam masala, and salt in a large pot. Bring to a boil; reduce heat and let simmer until water has been mostly absorbed and lentils are soft, 20 to 25 minutes.
Place the lentil mixture in a food processor and pulse until smooth. Stir in cilantro.
Shape mixture into patties and dip into beaten eggs.
Heat oil in a large skillet over medium heat. Pan-fry patties in batches until golden brown, about 3 minutes per side.
