For berries: Combine blueberries, raspberries, blackberries, powdered sugar, and 1/2 cup water in large saucepan. Bring to simmer, stirring until sugar dissolves. Reduce heat to medium and simmer until berries are soft but still intact, stirring occasionally, about 8 minutes. Transfer mixture to large bowl; stir in lime juice. Cool to room temperature. Stir strawberries into berry mixture. Chill until cold, about 4 hours. DO AHEAD: Can be made 1 day ahead. Cover and keep chilled.
For syrup and ladyfinger layer: Combine 1/3 cup water, 1/3 cup sugar, and lime peel strips in small saucepan. Bring to boil over medium heat, stirring until sugar dissolves. Pour syrup into bowl. Cool to room temperature; discard lime peel.
Using pastry brush, brush ladyfingers on both sides with syrup. Arrange in single layer in 13x9x2-inch glass baking dish, cutting to fit and covering bottom of dish completely. Pour chilled berry mixture over.
For mascarpone topping: Combine mascarpone and cream in large bowl. Using electric mixer, beat until smooth and slightly thickened (do not overbeat or mixture may curdle). Add Lime Curd; beat just until blended. Drop mascarpone topping by large spoonfuls over berry mixture. Spread evenly, covering berries completely. Cover and chill at least 8 hours. DO AHEAD: Can be made 1 day ahead. Keep chilled.
Spoon tiramisù into bowls and serve.
* Available at some supermarkets and at specialty foods stores and Italian markets.
** An Italian cream cheese; sold at many supermarkets and at Italian markets.