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. 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. 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 tiramisu 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.