If you were willing to pay approx. 8–9 euros for lunch, there would be lots of good options. For example:
- Satkar Kamppi (Nepalese restaurant, tripadvisor, home page): vegetarian options in the lunch menu for 8.40 euros.
Note that the quoted prices in the lunch menus are precisely what you will pay (assuming you drink water). There are no additional taxes or service fees, and you don't add a tip in Finland. You can try to use eat.fi to find good restaurants in Helsinki (you can, e.g., search for "vegetarian friendly" restaurants with high ratings that are open right now).
Your budget of 6–8 euros will be a bit more tricky (other than self-catering). Some suggestions in this price range:
Armas Pikaruokala (tripadvisor, home page): very good vegetarian lunch ("kasviskebab") for 8 euros.
Student cafeterias (home page): lunch starting from 7 euros (cheaper if you have some connection with the university), healthy (not necessarily delicious), and there are vegetarian options. I think one of the cafeterias ("Ylioppilasaukio", in the middle of downtown Helsinki) also serves lunch on Saturdays.
For very simple self-catering, buy a vegetarian Thai cube from a local supermarket. You will need only a microwave oven and a fork. The price should be less than 4 euros.