People in middle eastern countries have been eating labneh for thousands of years and most traditional methods for making it do not call for refrigeration. And, many people today make labneh by suspending the yogurt in a cloth over their kitchen sink. So, technically, no. You do not have to place the bowl of yogurt in the refrigerator while waiting for the whey to drain out. Having said that, I always do. Yogurt transforms into labneh just as well in the refrigerator as it does at room temperature. So, for me, better safe than sorry (especially when it comes to commercially made yogurt) is the right move. Just to be clear: prepared labneh MUST be refrigerated. See the section above for more instructions about how to store homemade labneh.