In a large, resealable plastic bag or plastic container with a lid, mix apples with the juice of 1/2 lemon. Freeze for several hours or overnight.
In a small saucepan, bring water and sugar to the boil. Reduce heat, and simmer for 5 minutes. Remove from heat, and stir in honey. Cool completely.
Place apple in a blender, and liquidise them with juice of 1 lemon and the cooled sugar syrup until as smooth as possible. The peel will add texture, and prevent the mixture from being completely smooth.
Transfer the mixture to an ice cream machine and freeze according to directions. Leave the sorbet out to soften 10 minutes prior to serving.