Remove the tops from the strawberries and cut the larger ones in half. In a large mixing bowl mix together roughly 3/4 of the strawberries with 1/4 cup of sugar, 4 tablespoons of balsamic vinegar and a generous pinch of salt. Toss well to evenly coat all the berries. Spread out the strawberries onto a large baking sheet lined with parchment paper (a 18x13 inch sheet is good) . Roast the strawberries for 20 to 25 minutes or until the fruit is softened and turned a deep purple red.
In a small pot mix together 1/2 a cup of sugar and 1/2 a cup of water. Turn the stove onto low heat and cook the mixture until all the sugar dissolves and you are left with a clear, slightly viscous syrup. Then immediately turn off the stove and let it sit for a few minutes.
Transfer the roasted strawberries to a blender. Add the syrup, lemon juice, and the rest of the non-roasted strawberries to the blender, and blend well. There should be about 4 cups of puree.
Strain the sorbet through a fine-mesh strainer into a large measuring cup. Cover the cup with plastic wrap and chill the sorbet till cold, about two hours but preferably overnight.
Pour the base into the ice cream machine and churn according to the machine directions, or until the sorbet has become thick (about 25 minutes).
Put the sorbet into a freezer-safe container, and cover with plastic wrap to prevent ice crystals from forming.