Pour water into a pot and bring to boil. Add salt and cook the beet until tender. Cooking time will vary depending on the size of the beet.
Once the beet is well cooked, take out of the pot and let cool on a cutting board before peeling.
Mix beet with feta cheese in a food processor until smooth and set aside.
Spread beet purée on the wrap.
Cut avocado in quarters lengthwise and brush with lemon juice to prevent discolouration.
Arrange avocado quarters, sunflower seeds, and arugula on the wrap.
Season with salt and pepper to taste before rolling up.