In a mixing bowl combine the chicken thighs, soy sauce, lemon or calamansi juice, half of the chopped onion, and the minced garlic. Marinate for at least 30 minutes.
Heat the cooking oil in a large pot over medium heat. Sauté the remaining chopped onion until soft and translucent, about 3–4 minutes.
Add the marinated chicken to the pot (reserve the marinade) and brown the pieces on all sides, about 5–7 minutes.
Pour the reserved marinade and the tomato sauce into the pot. Add the bay leaves and black pepper, then bring the mixture to a simmer.
Cover the pot, reduce heat to low, and simmer the chicken until tender, about 30 minutes.
Add the cubed potatoes and the cubed red and green bell peppers to the pot. Continue cooking until the potatoes are fork-tender, about 10–15 minutes.
Remove bay leaves, taste and adjust seasoning if needed, then serve the chicken asado hot with steamed rice.