Add 2 tablespoons of lime juice, paprika, garlic powder, salt, and black pepper in a large mixing bowl and mix well.
Add the chicken wings and coat into the mixture. Transfer to the refrigerator and marinade for at least 1 hour.
Drizzle vegetable oil in a large pot and heat it on medium.
Add the chopped onion and diced green pepper. Cook for about 6-8 minutes or until the onion is softened while stirring occasionally.
Add the potatoes and carrots to the pot.
Add the marinated chicken wings and bay leaves, and then season with the red pepper flakes and ground allspice.
Pour the remaining lime juice and water and bring the mixture to a simmer.
After simmering, lower the heat, and cover the pot with a lid.
Keep simmering the dish until the chicken is cooked and the vegetables have become tender, which should take 35-40 minutes.
Remove the bay leaves before serving.