Sprinkle the gelatin over ½ cup cold water to soften.
Combine the sugar, salt, and 1 cup water in a saucepan, and bring to a boil over medium-high heat.
Stir the softened gelatin into the pan. Cook for 1 minute, or until the gelatin dissolves.
Remove the pan from the heat, and stir in 1 ½ cups cold water, along with the lime juice, basil, and lime zest.
Transfer the hot liquid to a storage container, and refrigerate uncovered until it is completely chilled (below 40 degrees).
Freeze the mixture in an ice cream maker according to the manufacturer’s instructions. Serve immediately for a soft sorbet, or transfer the mixture to an airtight storage container and freeze until hard. Allow the sorbet to sit at room temperature for 15 minutes before serving if frozen solid.