Preheat oven 350°F.
Prepare 13”X9” baking pan. Line with parchment paper. Grease and flour. Set aside.
Using a small bowl, add zest to sugar and press between fingers until sugar becomes pale yellow and fragrant. Set aside.
Sift flour with baking powder. Set aside.
Place jam in small bowl and stir to loosen. Set aside.
Beat eggs in stand mixer with wire whisk for a few minutes.
Gradually add lemon sugar and beat until creamy, doubled in volume, and pale yellow, about 5 minutes.
Reduce speed a little and gradually add oil and liqueur.
Stop mixer and change the whisk attachment to paddle. On medium speed, slowly add flour mixture and mix until no flour streaks remain. Do not overbeat. (If using hand mixer, use beaters to mix in flour but when dough becomes too stiff, incorporate remaining flour with fork.
Transfer about two-thirds of batter into pan and spread evenly, including the corners.
Spread jam on surface, leaving some dollops.
With remaining batter, prepare the lattice top. Flour counter and scrape bowl. Divide batter into quarters and carefully form short ropes. Use enough flour to keep batter from sticking to fingers. Carefully lift rope and stretch it between fingers to lattice over jam, starting from one side to the opposite. If rope breaks, just re-attach it. Continue with about 5 strips across one way and 5 strips in the opposite directions to form a lattice-type crust. Use any remaining batter to shape little balls and place in open spaces of lattice.
Bake for 30-35 minutes or until lightly golden and jam is bubbly. Use a toothpick to check for doneness. Do not overbake. Remove cake from oven and remove from pan to cool on rack.
To serve, dust with icing sugar.