Sauté the onion and leeks in the oil over medium-high heat until they are translucent. Transfer to a stock pot and add the potatoes, carrots, pepper, and water. Bring to a rolling boil and boil for 5 minutes, then reduce the heat and cover. Allow the soup to simmer on low for 15 to 20 minutes.
Turn off the heat and uncover the soup. Test the potatoes to make sure that they are done. Once they are cooked thoroughly, allow the soup to cool for a few minutes, then stir in the feta and lemon juice. Serve warm with tortillas or French bread.