Combine honeydew melon, sugar, and lemon juice in a blender; process until smooth and sugar dissolves. Stir in prosecco; pour into an 11 x 7-inch baking dish. Cover and freeze 45 minutes. Stir honeydew mixture with a fork every 45 minutes until completely frozen and slushy (about 4 hours). Remove honeydew melon mixture from freezer; scrape mixture with a fork until fluffy.