Combine sugar and water in a small saucepan, and bring to a boil over high. Reduce heat to medium, and cook, stirring constantly, until sugar dissolves, about 5 minutes. Remove from heat, and cool completely, about 1 hour.
Process mashed avocado, simple syrup, and lime juice in a food processor or blender until completely smooth, about 20 seconds. (Add up to 2 tablespoons water if needed to achieve a thick but pourable consistency.)
Pour mixture evenly into 10 (2-ounce) plastic ice pop molds. Insert pop sticks, and freeze until solid, about 4 hours.
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