Dissolve the sugar in water in a small pot over medium heat, about 7 minutes.
While the sugar water mixture (simple syrup) is cooling, juice the limes. I have a handy dandy citrus press that works really well.
When the juice is cooled (about an hour), add the juice to the simple syrup and put in fridge overnight.
Heat blackberries in a small pot over medium heat.
Add sugar and water.
Cover and cook, stirring and crushing the blackberries as you go, for about 30 minutes.
Add the sorbet mixture to you ice cream maker and let it do its job.
(I like my sorbet to be hard, so I always put it in the freezer overnight after making in the machine, but you can eat it now if you'd like).
Graham Cracker Crumbs
Add the graham crackers to a blender/food processor and buzz until fine dust.
Add the melted butter and buzz again to make a sand-like mixture.
Lay out the mixture on a baking dish and bake at 350 for 10 minutes.
Swirl your caramel sauce on the plate. I like trying to make a design with it! Spread some of the graham cracker crumbs on the plate, add a scoop of the lime sorbet and then drizzle with the blackberry sauce