Place grated cucumber in a mesh strainer over top of a bowl and sprinkle with a little salt. Allow to sit for half hour or so. You will want to get as much juice as possible out of the cucumber before adding it to the sauce by either squeezing it by hand or using a cheese cloth.
Combine the squeezed cucumber, Greek yogurt, lemon juice, zest, garlic, dill, salt and pepper. Mix well and add salt and pepper as needed.
Cover and refrigerate for at least an hour before serving, but allowing flavors to marry overnight is even better.