Mix lemon cake mix, eggs, and vegetable oil in a bowl until thoroughly combined. Stir apricot nectar into the batter and mix well.
Pour batter into the prepared cake pan.
Bake in preheated oven until the cake is lightly browned at the edges and the top springs back when lightly pressed, about 30 minutes. A toothpick inserted into the center of the cake should come out clean or with moist crumbs. Check for doneness after 20 minutes.
Cool cake completely.
Mix confectioners’ sugar with lemon juice, mixing juice in about 1 tablespoon at a time, until the frosting is fluid and easy to spread. Frosting should run slightly but not be a thin runny glaze.
Spread frosting on cooled cake and sprinkle with lemon zest to serve.