Make the sugar syrup: Place xylitol (or sugar) and water in a small saucepan. Heat over medium-high heat until xylitol is completely dissolved. Remove from heat and cool slightly.'

Make the strawberry puree: Place strawberries and water in a blender or food processor. Blend on high speed until completely smooth, scraping down the sides if necessary.

Prepare the lemonade: Place lemon juice, 5 cups water, sugar syrup, and strawberry puree in a gallon-sized container. Screw lid on and shake lemonade until combined. Serve lemonade over ice.