Heat the oil and 1 tablespoon butter in a large skillet over medium heat. Add the garlic and cook until fragrant, about 1 minute. Add the green beans, then season with salt and pepper and stir to combine.
Add the stock, then bring to a simmer and cover the skillet. Cook until the green beans are bright green and just slightly tender, about 5 minutes. Uncover the skillet and cook until the liquid evaporates and the green beans are tender, 10 minutes more. Stir in the lemon juice and remaining tablespoon butter and season with additional salt and pepper.