Cook apricots and water in a saucepan over medium heat for 20 minutes.
Puree mixture in blender or the work bowl of a food processor fitted with a metal blade.
Strain into a mixing bowl.
Stir in sugar and lime juice.
Pour into an 8-inch square pan and freeze until plushy.
Return mixture to blender or food processor and prqcess until smooth and creamy.
Return to pan and freeze again.
Remove from freezer 15 minutes before serving.
STRAWBERRY ICE Rinse and hull 1 quart of strawberries.
Place in blender or work bowl of a food processor fitted with a metal blade.
Process until pureed.
Add 1/2 cup strawberry preserves and 1 tablespoon fresh lemon juice.
Process until mixed thoroughly.
Strain into 8-inch square pan.
Freeze and proceed as directed above.