Pour just enough water in the double-boiler pan so the water level is right below the bottom of the mixing bowl when it is sitting in the pan. Separate the eggs, putting yolks into the large bowl of the double boiler and the whites into another stainless-steel bowl for whipping by hand or with an electric mixer.
To make the base for the tiramisù, heat the water in the double boiler to a steady simmer. Off the heat, beat the egg yolks with 1/4 cup of the sugar and 1/2 cup of the limoncello until well blended. Set the bowl over the simmering water, and whisk constantly, frequently scraping the whisk around the sides and bottom of the bowl, as the egg mixture expands and heats into a frothy sponge, 5 minutes or longer. When the sponge has thickened enough to form a ribbon when it drops on the surface, take the bowl off the double-boiler pan and let it cool.
When the cooked limoncello sponge (or zabaglione) is cooled, scrape about a third of it over the mascarpone, and fold it in with a large rubber spatula. Fold in the rest of the zabaglione in two or three additions. Now fold in the whipped egg whites in several additions, until the limoncello-mascarpone cream is light and evenly blended.
Pour some of the cooled syrup, no deeper than 1/4 inch, into the shallow-rimmed pan to moisten the ladyfingers (savoiardi). One at a time, roll a ladyfinger in the syrup and place it in the casserole or baking dish. Wet each cookie briefly—if it soaks up too much syrup, it will fall apart. Arrange the moistened ladyfingers in neat, tight rows, filling the bottom of the pan completely. You should be able to fit about twenty ladyfingers in a single layer.