Combine Ingredients: Place the frozen (or fresh) peaches, granulated sugar, water, and lemon juice into a medium saucepan.
Heat and Stir: Set the saucepan over medium heat. Stir the mixture to combine all the ingredients.
Bring to a Simmer: Adjust the heat to bring the mixture to a simmer or a low, rolling boil. Continue to cook at a simmer, stirring often to prevent sticking and to help dissolve the sugar.
Cook and Smash Peaches: Cook the mixture for 10 to 15 minutes. While cooking, mash the peaches to break them apart using a wooden spoon or potato masher.
Strain the Syrup: Remove the saucepan from heat. Pour the mixture through a mesh sieve into a heat-safe container to strain out the peach solids, leaving you with the sweet peach syrup.
Chill or Use Immediately: Refrigerate the syrup to chill before use. Store any leftovers in the refrigerator for up to a week.