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 necessary. It should be the consistency of pancake batter.
Meanwhile, mix the mayonnaise with the olives and lemon juice in a small bowl. Thin with 1 to 2 tablespoons water, if you like. Keep covered in the refrigerator until ready to serve the zucchini. Makes about 1 1 4/ cup.
Cut the zucchini into sticks that measure 3/4-inch wide and 4 inches long. Heat 3 to 4 inches of oil in a large deep saucepan until a deep-fat frying thermometer reaches 360 degrees F. 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 sieve and shake to remove excess flour. Working in batches, dip in the batter, letting the excess drip off. Fry 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.