Can one veggie smoothie help lose weight?

No: If you replace your high carb breakfasts with a low-carb veggie smoothie daily then perhaps that would help, but a single veggie smoothie will not help lose weight.

Need the fiber.: While fruit or vegetable are relatively nutritious and low-calorie, they tend to eliminate the fiber benefit of the fruit. Fiber helps us stay full in between meals so we eat less. For weight loss, I'd rather see you eat the fruit.