Set the yogurt in a sieve set over a bowl to strain and come to room temperature, about 1 hour.
Fill a large pot with water and bring to a boil. Season generously with salt. Add fettuccine and cook until al dente, about 2 minutes less than the box instructions. Drain, reserving 1 cup pasta water.
Combine feta, yogurt, garlic, lemon zest and juice, olive oil and half the herbs in a large bowl, then season with salt and pepper. Mix until well blended.
Add the hot cooked pasta and toss to coat. Add some pasta water until sauce is at desired consistency. Taste and adjust seasoning. Transfer to serving bowls and garnish with Pecorino-Romano and the remaining chopped herbs.