Whisk 1 cup of the flour with the beer in a large bowl until smooth. Pour through a strainer into another bowl and let stand for 1 hour. Thin with additional beer just before frying if thicker than pancake batter. Meanwhile, mix the mayonnaise with the olives and lemon juice in a small bowl. Thin with 1 to 2 tablespoons water if needed.

Keep covered in the refrigerator until ready to serve the zucchini. Cut the zucchini into sticks that measure 1/4 inch wide and two inches long. Heat two inches of oil in a large deep saucepan until a deep fat frying thermometer reaches 350ºF. 

Combine the remaining 1/2 cup flour with salt and pepper in a shallow bowl or pie plate. Add the zucchini and toss to cover in flour. Transfer to a strainer and shake to remove excess flour. Working in batches, dip in the batter, letting the excess drip off.

Fry in batches until golden brown and crisp, about 3 minutes. Drain on paper towels and sprinkle with salt. Serve the olive mayonnaise on the side for dipping.