Combine 1 cup berries and sugar in a small bowl and let sit, stirring occasionally until the sugar has begun to dissolve, about 10 minutes. Transfer the berry mixture to a food processor or blender and process until smooth.
Meanwhile, combine buttermilk, half and half, lemon juice, vanilla, and salt in a medium bowl. Press the strawberry mixture through a fine-mesh sieve into the bowl. Stir, cover, and chill for at least 2 hours or up to 1 day.
Whisk the sherbet mixture and pour into the canister of an ice cream maker. Freeze according to the manufacturer's directions. During the last 5 minutes of freezing, add the remaining 1 cup chopped berries. If necessary, place the sherbet in the freezer to firm up before serving.