Place strawberry slices in a large glass bowl. Stir in sugar and lime juice, if desired. Allow to stand for 30 minutes.
For filling, in a large bowl combine the cream cheese, powdered sugar, the 3 tablespoons liqueur, 2 teaspoons seedless strawberry jam, and a couple drops of red food coloring (if desired); beat with an electric mixer on medium speed until blended and smooth. Stir in 1/2 cup of the whipped dessert topping and 2/3 of the strawberry mixture. Set aside.
For the frosting, in another bowl combine the remaining whipped dessert topping and 2 tablespoons liqueur. Set aside.
Place 1/3 of the ladyfingers in a layer on a serving platter and the remaining 2/3 in 2 separate layers on large dinner plates. With a long-tined fork or a skewer, poke holes in tops of all 3 layers of ladyfingers. In a small bowl combine the coffee and 2 tablespoons liqueur; drizzle over all layers. Spread the first layer with half of the filling. Arrange a second layer and spread on the remaining filling. Arrange top layer of ladyfingers. Frost the top layer with the frosting and top with the remaining strawberry mixture. (If desired, cover and chill for up to 4 hours.)
To serve, cut cake into wedges. Makes 16 servings.