In a saucepan over medium heat combine first 3 ingredients (water to zest) and bring to a boil, stirring to dissolve sugar. Reduce heat and simmer 5 minutes. Remove from heat and let cool 5 minutes. Discard zest and stir in lime juice.
Puree 1 cup of the syrup with 3 1/2 cups of strawberries in food processor or blender. Stir mixture into remaining syrup. Pour mixture through a sieve into a medium bowl and discard solids. Cover and refrigerate for 2 hours or overnight.
Transfer mixture to ice cream maker and process following manufacturer's directions and then transfer sorbet to freezer container and freeze until firm (2-6 hours).
To serve, slice remaining strawberries and scoop sorbet into 8 dessert dishes and top with sliced strawberries.