Cook lamb in oil in a large Dutch oven over medium heat until browned. Add 3 cups water, squash, pinto beans, corn, pepper pod, salt, and pepper. Bring to a boil. Reduce heat; cover and simmer 2 hours.
Combine remaining water and flour; stir until smooth. Pour into stew; cook, stirring frequently, until thickened and bubbly. Remove pepper pod; discard.