Combine sugar, lime zest and lime juice in a heatproof bowl. Add boiling water and stir until the sugar has dissolved. Cover and refrigerate until chilled, about 1 hour or overnight.dd yogurt to the lime mixture and whisk until smooth. Pour into an ice cream maker and freeze according to manufacturer's directions. (Alternatively, freeze mixture in a shallow metal pan until solid, about 6 hours. Break into chunks and process in a food processor until smooth.)
Serve immediately or transfer to a storage container and let harden in the freezer for 1 to 1 1/2 hours. Serve in chilled dishes.