To make the thyme syrup, add the water to a small saucepan. Turn to medium-high heat and stir in the sugar. Stir often, until the sugar completely dissolves into the water and the syrup is clear, about 4 minutes. Once clear, let the syrup simmer for about 1 minute, until slightly thickened

Turn off the heat and add the thyme sprigs. Let cool completely while the thyme infuses the syrup, at least 30 minutes. Discard the thyme and strain the syrup if necessary to remove any stray leaves.

Add the strawberries, cooled and strained simple syrup, lemon juice, and ice to a blender. Puree on high for 30 seconds smooth. Pour into two glasses, garnish with a strawberry halves and thyme, and serve right away.