Line a colander with two layers of cheesecloth and place it over a medium bowl. Place the yogurt on the cheesecloth and cover the colander with plastic wrap. Allow yogurt to drain overnight.
Lay grated cucumber on a plate lined with paper towel; allow to drain 1 to 2 hours.
Combine the drained yogurt, cucumber, garlic, parsley, mint, lemon juice, salt, and pepper in a bowl. Refrigerate for at least 2 hours before serving.
