In a large bowl, combine the cubed cantaloupe with 1/3 cup of sugar. Cover and marinate at least 6 hours in the refrigerator.
In a saucepan over medium-low heat, simmer the marinated cantaloupe pieces in the juices of the marinade. Cook for 5 minutes, stirring occasionally, then remove and cool.
Puree the cantaloupe mixture in a blender or food processor. Add the lime juice and process again. Cover and chill for an hour.
In a large bowl, combine the half and half and coconut milk with the remaining 1/2 cup of sugar. Stir in the pureed cantaloupe gently to mix in.
Place mixture in the freezer for about 2 hours. Transfer to an ice cream maker and proceed with the manufacturer's instructions for making ice cream.
Place the cantaloupe ice cream into an air tight container and return to freezer for 2 hours before serving.