Grate the cucumber on the large holes of a box grater. Toss with half the salt and let stand in a sieve for 10 minutes.
Transfer the cucumber to a clean kitchen towel and squeeze out as much liquid as you comfortably can. Discard the liquid.
In a bowl, stir together the Greek yogurt, dill, lemon juice, garlic, remaining salt and a few grinds of black pepper.
Fold in the squeezed cucumber. Taste and adjust the lemon, dill or salt a little at a time.
Cover and refrigerate for 20 minutes if time allows. Stir once before serving. Pour away any liquid that collects on top.