I am not a vegetarian, but meals in regular restaurants in Peru will include very few (if any) vegetables, other than potatoes. I usually ate veggie at lunch, and then at a regular restaurant for dinner.
The owner is a former employee of Bircher Benner restaurant (an excellent but expensive vegetarian restaurant in Lima). For 8 soles (a little over $2US) you get an emoliente drink, a first course (usually a salad or soup), and the main plate and small dessert. You also get a plain, drinkable yogurt (add anise syrup from the pitcher on your table to add a flavor).
This was probably my favorite veggie restaurant in Lima and I went there most days. Every meal I had there was good. You can also order from the menu, but the set meal was a great value. Open daily 9am to 8pm. Closed Sundays; open limited hours on holidays.