Place sugar in a small pan with 3 Tbsp. water and lime juice and stir over medium heat until sugar has dissolved, about 3 minutes. Remove from heat.
Cut honeydew in half, remove seeds, peel and chop fruit. Transfer to a food processor, add reserved sugar mixture and salt. Process until slushy.
Transfer mixture to a 9-inch square metal baking pan and freeze for 1 hour. Stir with a fork to break up chunks around edges. Freeze until completely frozen, about 2 hours longer, stirring with a fork every 30 minutes to loosen ice crystals. Serve in chilled glasses or bowls.