Lava has three vegetarian dishes: vegetable risotto, a fresh summer salad (with tomatoes, asparagus and honey-glazed lemon fruits) and a tofu "cake" with mashed sweet potatoes served over a bed of salad. The salad that accompanies the tofu "cake" comes out topped with feta, but you can ask to leave that out. Otherwise, the dish is dairy-free.
I was surprised (and very pleased) to find such wonderful vegetarian options at a restaurant that otherwise serves Icelandic specialties (which tend to be the opposite of vegetarian). My tofu cake dish was remarkably good and I found the ambiance of Lava to be stunningly beautiful. In spite of the fairly high price (my tofu cake dish was approximately $18 USD) I think that Lava is by far the most worthwhile option for vegetarians and vegans visiting Blue Lagoon.