Saute the veggies. Heat the oil in a large pot over medium-high heat. Add the onion, carrots, and celery, and saute for 4 to 5 minutes, until softened. Add the garlic, Italian seasoning, salt, and pepper, and saute another 30 seconds.
Add more veggies. Add the potatoes, green beans, tomatoes, bay leaves, and broth. Stir together and bring to a boil, then reduce the heat to low, cover, and simmer for 20 minutes, until the potatoes are just fork tender.
Add the frozen veggies. Add the corn and peas, stir, and cook about 5 to 7 minutes longer.
Serve. Turn off the heat and stir in the lemon juice and parsley. Ladle the vegetable soup into bowls.