Wet large square of cheesecloth and wring dry. Line sieve with damp cloth; place sieve over bowl. Spoon yogurt into sieve, fold cheesecloth ends over yogurt, and chill overnight to drain.
Scrape drained yogurt into medium bowl. Mix in olives and lemon juice.
Do ahead: Can be made 1 hour ahead. Cover; chill.
Season with salt and pepper. Transfer to small bowl. Place on platter with flatbreads and/or crackers.
