Prepare watermelon: Line a baking sheet with parchment paper. Place watermelon on parchment in a single layer.
Freeze watermelon: Place baking sheet in freezer until watermelon is completely firm and frozen, at least 2 hours or up to 12 hours.
Blend ingredients: Process frozen watermelon, condensed milk, lemon juice, arrowroot powder, vanilla, and salt in a food processor until completely smooth, about 1 minute.
Freeze sherbet: Pour watermelon mixture into frozen freezer bowl of a 1 ½-quart electric ice cream maker; freeze according to manufacturer’s instructions. (Instructions and times may vary.)
Freeze until firm: Transfer mixture to a loaf pan or airtight container, and freeze until firm, at least 6 hours.