In a small saucepan, bring sugar and water to a boil. Stir occasionally until the sugar is completely dissolved. Add the peaches to the sugar mixture and transfer to a sealable container. Refrigerate for 5 hours (or more)
Strain peach mixture through a fine strainer over a medium bowl. Discard the peaches. Add half of the raspberries and lemon thyme sprigs. Gently mash berries with the back of a spoon so that they begin to juice. Pour into a pitcher through a fine strainer. Press through the strainer then discard the contents left in the strainer.
Add club soda to the pitcher with juice mixture and stir until combined.
Gently crush the remaining lemon thyme sprigs. Pour the juice mixture over ice into glasses and garnish with the remaining raspberries, lemon thyme and lime slice.
