In a blender combine mangoes, water, sugar, and lemon juice; cover and blend until smooth. Add yogurt; cover and blend until combined. Transfer mango mixture to a 3-quart rectangular baking dish. Cover and freeze about 3 hours, stirring two or three times, until edges are firm but center is still slightly soft.
Scrape mango mixture into large chilled mixing bowl. Beat with electric mixer on medium speed until smooth. Pour mixture into molds or paper cups. Cover with lids or, if using paper cups, foil. (Use a table knife to make a small slit in center of each foil section). Slide crafts stick through each hole and into center of fruit mixture in each cup. Cover and freeze overnight. Remove from mold or peel off paper to serve. Makes 12 to 16 popsicles.