In a large sauce pot, heat the olive oil over medium heat. Add the onions, carrots, celery, and salt. Sauté until tender.
Transfer sautéed vegetables to a blender, then add 3 1/2 cups or 2 cans of the diced tomatoes, sugar, black pepper, and cayenne pepper to the blender. Blend until smooth.
Return mixture to the pot and add rice, vegetable broth, and remaining 1 3/4 cups or 1 can of diced tomatoes. Bring to a boil, stirring regularly.
Reduce heat to a simmer and cover. Cook for 30-35 minutes, stirring occasionally, until the rice is tender and broth is rich and thick.
Add parsley and lemon juice, stir to combine. Serve.
