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. Can be made 1 day ahead. Cover and keep chilled.
Syrup and Ladyfinger Layer: Combine 1/3 cup water, 1/3 cup sugar, and lime peels 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" glass baking dish, cutting to fit and covering bottom of dish completely. Pour chilled berry mixture over.
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 leaast 8 hours. Can be made one day ahead. Keep chilled.
Lime Curd (MUST CHILL OVERNIGHT, SO PREPARE ONE DAY AHEAD): Place fine strainer over medium glass bowl. Melt butter in heavy medium saucepan over medium-low heat. Remove from heat. Add sugar, lime juice, lime peel, and salt; whisk to blend. Add yolks and whisk until smooth. Return saucepan to medium heat and whisk constantly until curd thickens slightly and leaves path on back of spoon when finger is drawn across and instant-read thermometer inserted into curd registers 165 degrees (do not boil), 10-12 minutes (mixture will not be as thick as traditional curd but will resemble slightly thickened sauce). Pour curd into prepared strainer; discard solids in strainer. Place plastic wrap directly onto surface of curd and chill overnight. Can be made one week ahead, Cover and keep chilled.