Another great dish we had in both Turkey and Greece on our annual sailing holiday, not to mention in Scotland.. It's best to use the "European / English Cucumber" as they call it in the USA. That's the long skinny one we always had fridge. You can certainly use the US cucumber (they tend to be a lot cheaper!) but remember to first scoop out the seeds before salting.
Toss the cucumber with some salt (not a lot, teaspoon or so) and leave in a colander in the sink to wilt for 15 to 30 minutes.
Mix the yoghurt, garlic, olive oil, lime juice, salt and pepper together while the cucumber is draining. Stir in the cucumber and adjust seasonings as needed.