Juice the oranges and the lemon. Strain out any pulp or seeds that are leftover. You can also use store bought orange juice and lemon juice if you want to skip the juicing step. Set aside.
Make the simple syrup. Add the water and the sugar and the thyme sprigs to a small sauce pan. Place over low heat and stir every once in a while until the sugar has dissolved completely (you don’t need to bring to a boil). Once the sugar has dissolved, taste it. If you like the thyme flavor, it’s good to go. If you want the flavor to be stronger, let it sit for a few more minutes.
Put the juice into a pitcher or large mason jar. Add simple syrup bit by bit until you reach desired sweetness. If you’re making cocktails, add 4 to 6 ounces of liquor to the pitcher or jar. Fill 4 glasses almost to the top with ice. Pour the juice/simple syrup/liquor mixture evenly into the glasses. Top with soda water. Stir and enjoy!