Combine the water and sugar in a large saucepan, and bring to a boil, stirring until the sugar dissolves. Remove from heat, and stir in honey. Cool completely.
Grate ginger; place ginger on several layers of damp cheesecloth. Gather edges of cheesecloth together; squeeze cheesecloth bag over a small bowl to measure 1 tablespoon ginger juice. (When I did this step, the juice came pouring out as I grated the ginger, so I was able to skip the straining part),.
Combine the sugar mixture, ginger juice, and lemon juice in a large bowl.
Pour mixture into the freezer can of an ice-cream machine, and freeze according to manufacturer's instructions. Spoon the sorbet into a freezer-safe container; cover and freeze 1 hour or until firm.
*OR* if you don't have an ice cream machine, stir the sorbet every half hour or so to as it is freezing (to break the ice crystals and prevent it from separating) until it reaches the desired consistency. You may have to run it through the blender if it freezes too solid or if it separates into its components; you may also want to take it out of the freezer and leave it in the fridge for 20 minutes immediately before serving to soften it up.