Preheat the oven to 350 degrees F (175 degrees C). In a medium bowl, stir together the flour and sugar. Cut in butter until the mixture resembles coarse crumbs. Press into the bottom of a 9x13 inch pan.
Bake for 12 to 15 minutes in the preheated oven, or until firm. While the crust is baking, place apricots in a saucepan with enough water to cover. Bring to a boil, and cook for 10 minutes.
Drain, reserving 1/2 cup of the liquid. Return the apricots and reserved liquid to the pan, and stir in the lemon zest. Mix together the sugar and cornstarch, and stir into the apricot mixture. Bring to a boil, and boil for 1 minute. Remove from heat and allow to cool. Spread onto the prepared crust, and sprinkle the walnuts over.
Bake for 20 to 25 minutes in the preheated oven, or until firm to the touch. Cool completely before cutting into bars.