Preheat the oven to 350 degrees F. Grease three 8-by-4-inch loaf pans and line them with parchment paper that comes at least 2 inches up the long sides of the pan. If you don't have 3 loaf pans, you can bake the layers in batches.
In a large bowl or in a stand mixer fitted with a whisk attachment, beat the egg whites to soft peaks. With the mixer running on medium, gradually add 2 tablespoons of the sugar. Increase the speed to medium high and beat to stiff peaks. Set aside.
In a large bowl or in a stand mixer fitted with a paddle attachment, beat together the butter, almond paste, salt and remaining 1/2 cup sugar on medium-high speed until light and fluffy, 2 to 3 minutes. Reduce the speed to medium and add the yolks one at a time, beating well after each addition. Beat in the lemon juice and almond extract, then reduce the speed to medium low and gradually add the flour. Mix to combine. Use a rubber spatula to fold in the whites.
Transfer one-third of the mixture to one of the loaf pans and use a small offset spatula to spread it out evenly. Transfer another third of the mixture to a separate bowl and fold in the green food coloring. Fold the red food coloring into the remaining third. Transfer these into the remaining 2 loaf pans, spreading them out evenly.
Bake until the tops are just set and no longer shiny; begin checking for doneness at 12 minutes. Let cool in the pans for 5 minutes, then lift them out and place on a wire rack to cool completely.
Stack up the loaves (from bottom to top: green, white, red) with 1 1/2 tablespoons jam between the layers. Wrap the loaf firmly in plastic wrap and refrigerate for at least 4 hours and up to overnight.
Melt the chocolate in a double boiler or by microwaving it in 30-seconds increments, stirring after each. Remove it from the heat and stir continuously until it is no longer hot. Spread it over the top and sides of the cookie loaf and refrigerate to firm up for about 15 minutes. Cut into 1-inch squares.