In a large skillet, heat the extra-virgin olive oil over medium heat. Add the chopped onion and minced garlic and cook until the onion is soft and translucent about 5-7 minutes.
Add the diced tomatoes, salt, and pepper to the skillet. Cook until the tomatoes have released their juices and the mixture has thickened slightly about 10-15 minutes.
Add the green beans to the skillet and stir well to coat with the tomato mixture. Pour the water over the green beans and cover the skillet with a lid. Cook until the green beans are tender, occasionally stirring for about 20-25 minutes.
Once the green beans are tender, remove the lid and continue cooking until most liquid evaporates about 5-10 minutes.
Remove from heat and let cool slightly. Serve warm or at room temperature, garnished with lemon wedges.