Rinse the blackberries, then combine in a blender with the water and lemon juice. Purée until smooth, then press the mixture through a sieve to grab the seeds.
In a saucepan, whisk together the blackberry juice, sugar and syrup. Tie together the thyme sprigs and add to the pan. Bring to a boil and reduce to a simmer. Let cook for 1 to 2 minutes, until the sugar is fully dissolved. Remove from the heat, discard the thyme sprigs, and place in the refrigerator to chill completely, at least four hours or overnight.
Freeze the sorbet mixture according to your ice cream maker’s directions.
Recipe adapted from naturallyella.com