1. Stir yogurt and salt thoroughly in a medium-sized bowl. Place a large piece of cheesecloth in a colander, so the edges hang over the sides, and set the colander in a bowl. Pour the yogurt into the cheesecloth, fold it over to cover completely. Place something heavy on top of the cheesecloth (a couple of jars or cans, for example), and let the yogurt drain in the refrigerator for at least 1 day (up to 2 days).
2. Meanwhile, heat the oil over medium heat in a small saucepan with a lid for about 7 minutes, until small bubbles begin to form. Remove the saucepan from the heat, add the thyme sprigs and orange strips, cover with the lid, and let the oil infuse, preferably overnight, but 30 minutes will suffice.
3. Prepare the berry purée the next day: Put 50g blackberries, 100g raspberries, and 100g strawberries in a food processor with the sugar and lime juice, and blend thoroughly. Place all the remaining berries in a large bowl with the purée, and gently toss. Serve the berries immediately, or refrigerate for a couple of hours and then bring to room temperature before serving.
4. Spread the labneh on a large platter. Top with the berries, and sprinkle with lime zest. Drizzle with 2 tbsp of the orange oil, and garnish with a couple of the orange strips and the extra thyme leaves.