In a small bowl, whisk together the yogurt, olive oil, vinegar, lemon juice, lemon zest, garlic, and dill. Salt and pepper the mixture to taste.
Peel the cucumbers as desired. Fully peel to remove all bitterness or leave them on, up to you. If you are using conventional cucumbers instead of English, I recommend peeling and removing the seeds from each of them. Then thinly slice the cucumbers using a mandolin, food processor, or by hand.
Do the same to the radishes. I prefer the food processor as the radishes are too small for a mandolin and you will get consistent slices. If you like your radishes less peppery, peeling them will cut down on the bite.
Keep the cucumbers and radishes together in a large serving bowl. Just before serving, mix the veggies with the yogurt dressing. Taste again and adjust the salt and pepper as needed.
You can do the above step up to 2 hours in advance, storing the mixture in the refrigerator. But no longer. The cucumbers will start to release water and the dressing will become watered down and runny.
Garnish the salad with some freshly cracked pepper and fresh dill.