Combine the sugar and water in a small saucepan over medium heat. Stir until the sugar is completely dissolved, about 5 minutes. Set aside and cool to room temperature.
Using a blender, pulse guava pulp until smooth. Add cooled syrup, a little at time, until sweetened to taste. Please note that it will lose some of its sweetness when it’s completely frozen. Blend in the lime zest and lime juice, also to taste.
To make granizados, pour guava mixture into a shallow metal or glass baking pan (9x13x2inches). Cover with aluminum foil and allow to set in the coldest part of your freezer for about one hour.
Using a fork, scrape the ice crystals that have formed into the center of the pan, mashing and blending them in as you go. Cover and return to the freezer. Repeat every 30 minutes or so until uniformly frozen about 2-3 hours depending on your freezer.
Serve immediately or cover tightly and freeze overnight. When ready to serve, use a fork to shave off ice crystals and scoop into dessert glasses.