In a large pot, combine water, onion, garlic, celery, carrot, potato, bay leaf, salt, and pepper. Bring to a boil, then reduce heat and simmer for 15 minutes.
Add broccoli florets and simmer for another 5-7 minutes, or until tender-crisp.
Remove from heat and discard bay leaf. Carefully transfer the soup to a blender (or use an immersion blender) and blend until smooth.
Return the soup to the pot and stir in nutritional yeast and lemon juice. Taste and adjust seasonings as needed.