Place the peaches in a small saucepan and, if the peaches are ripe, add a splash of water to the pan.If the peaches are not yet ripe, add enough water to just cover the bottom of the pan.
Cover the pan and bring to a boil. Remove the lid, reduce the heat and simmer for 5 minutes.
Mash the peaches with a potato masher and remove the pan from the heat.
Strain the mixture through a fine mesh sieve—using a spatula to push the remaining juice out of the peach mash.
Add the sugar and lemon juice to the warm peach juice.
Stir to dissolve, then let cool to room temperature.
Make sodas by adding 2 tablespoons of syrup to an 8-ounce glass of club soda.
Add more syrup to taste, if desired.