Grate the cucumber using the large holes of a box grated and place in a fine mesh sieve. Allow the cucumber to sit in the sieve for 30 minutes, pressing down on the cucumber with a paper towel to release some of the water.
Combine the yogurt, sour cream, garlic, olive oil, vinegar, dill, lemon zest and juice in a medium bowl.
Fold in the drained cucumber and refrigerate for 1 hour covered with plastic wrap.
Serve immediately, drizzled with olive oil, if desired. Or transfer to an airtight container and store in the refrigerator for up to 3 days. Stir before serving.