Heat olive oil in a large pot over medium heat. Add turkey, onion, green bell pepper, and garlic; cook and stir until turkey is browned and onion is translucent, about 5 minutes.
Stir tomatoes, celery, cumin, chili powder, bay leaf, and basil into the pot. Pour in water; cover and simmer until celery is tender and chili has reached desired thickness, 10 to 15 minutes. Stir in navy beans and lima beans; cook until heated through, 5 to 10 minutes. Season with salt and pepper.