Line a rimmed baking sheet with parchment paper. Place the cubed honeydew melon onto the baking sheet, leaving space in between the cubes to allow for even freezing. Freeze the honeydew overnight, or until completely frozen (about 4-6 hours).
Place the frozen honeydew into the bowl of a food processor, along with the lemon juice, honey, and water; pulse until the honeydew becomes crumbly.
You may need to add more water until the mixture is smooth, but not slushy. You're looking for a soft sorbet texture at this point. Taste the sorbet, add additional honey if needed.
Serve immediately, or store in the freezer in an airtight container for up to 2 weeks