1. 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.
2. Meanwhile, mix the mayonnaise with the olives and lemon juice in a small bowl. Thin and 1 to 2 tablespoons water, if you like.
3. Keep covered in the refrigerator until ready to serve the zucchini.
4. 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 35 degrees F.
5. Combine the remaining 1/2 cup flour with salt and pepper in a shallow bowl or pie plate. the zucchini and toss to cover in flour.
6. Transfer to a strainer and shake to remove excess flour. Working in batches, dip in the batter, letting the excess drip off.
7. 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.