Heat the oven to 275 degrees with the rack in the lower-middle position. Heat three tablespoons of the oil in a Dutch oven over medium heat until it shimmers but does not smoke.

Add the onion and cook until softened and translucent, about 5 to 7 minutes. Stir in the garlic and oregano and cook until they become fragrant.

Stir in the water, green beans, potatoes, and baking soda and bring the liquid to a simmer. Reduce the heat to medium-low and cook for 10 minutes, stirring occasionally to ensure the potatoes don't stick to the bottom.

Stir in the tomatoes and their juice, tomato paste, salt, and pepper. Cover the pot and transfer it to the oven to cook until the sauce has thickened and the beans are tender enough to be easily cut with the side of a fork, 40 to 50 minutes.

Stir in the basil and lemon juice, adjusting the acidity to your preference. Transfer the braise to a serving bowl and drizzle with the remaining two tablespoons of oil. Serve warm.