In the bowl of a stand mixer add the lemon zest and sugar. Beat for about 2 minutes on high to release the lemon oils into the sugar.
Add the butter, beat until well combined.
Add the eggs and vanilla, one at a time, beating well between additions.
Add the lemon juice, beer and olive oil , beating until well combined, scraping the bottom of the mixer to insure all ingredients are well incorporated.
Stop the mixer and sprinkle with flour baking powder, baking soda and salt, sitr until just combined.
Pour into a large loaf pan that has been greased.
Bake at 325 for 55 o 60 minutes or until cake is golden brown and tooth pick inserted in the center comes back with just a few crumbs attached. Allow to cool completely.
Stir together the powdered sugar lemon juice and salt to make a thick paste. Spread over the top of the cake, chill until set about 3 hours. Cake is best made a day ahead of time.
Substitute all of some of the beer to increase the beer flavor.
Notes
Substitute all of some of the lemon juice in the glaze to increase the beer flavor.