In a food processor, combine the garlic and basil (saving a little basil for garnishing) and pulse to mince. Add the lemon juice, oil, avocado, a 1 tablespoon water and process until smooth, stopping to scrape down the bowl as needed add a dash more oil if it's too thick. Season with salt and pepper to taste.
Drain the pasta and place it back in the pot. Add the avocado sauce and stir.
Garnish with pepper, lemon zest, and fresh basil leaves.
For an extra light version of this dish, use zucchini noodles instead of pasta.