In a medium saucepan, combine berries, honey and 1 cup (240ml) of water. Simmer over medium heat until honey is fully dissolved, about 4-5 minutes, stirring frequently.
Transfer the mixture into a blender, add the lemon juice and blend.
Strain the mixture through fine mesh sieve to remove the seeds.
Cool to room temperature, and then refrigerate for at least 2 hours, or overnight.
Pour the cooled mixture into the ice cream machine and follow the manufacture’s instructions.
Freeze the sorbet for firmer texture.