Line a sieve with a double layer of paper towels and set over a bowl. Whisk yogurt with salt and spoon into sieve. Let drain, covered and chilled, at least 12 hours and up to 24.
Meanwhile, toast sesame seeds in a dry small heavy skillet, shaking skillet occasionally, until golden, about 2 minutes. Whisk together oil, mint, and thyme in a bowl, then add toasted sesame seeds and chill, covered, up to 24 hours.
Bring sesame mixture to room temperature, then drizzle it over lebneh (thickened yogurt).
