Using a rubber band,secure cheesecloth, a paper towel, or a coffee filter over a small bowl, ensuring it does not touch the bottom of the bowl. Pour the yogurt onto the filter and refrigerate overnight to strain out the liquid.
In a blender, blend the strained yogurt, milk, 1 cup water, and ice until smooth. Remove and reserve 1/2 cup of the yogurt mixture for garnish. Reserve 1/2 cup of the strawberries, add the remaining strawberries to the blender with the yogurt mixture, and blend until the lassi is smooth.