Altitude is a major dimension you are not using in your example. In real life aircraft, we have rules such as "aircraft flying east or north fly at odd numbered thousands, such as 3500 or 5500 feet, those flying west or south fly at even numbers, such as 4500 or 6500 feet."
You also don't need flying lanes to be as narrow as the highway lanes on the ground. They can spread out horizontally, because they are not constrained by ground buildings, except perhaps skyscrapers, and they can be stacked vertically, as described above. And in many cases, you may not need defined lanes at all, unless it is really congested.
Of course individual flying animals don't need as much separation as thatplanes, but at the same time, may not have as precise altitude control. But most large flying animals (i.e. birds) are also very good at collision avoidance. You mention bugs, but I'm ignoring those as an example because none on earth have that level of intelligence. (Though dragonflies are superb flyers, skilled in avoidance and intercept.) So you may not need as strict separation as we have for vehicles. For instance we have very strict separations when driving vehicles moving 65MPH, but very loose guidelines in pedestrian spaces where we are walking 5MPH, because our brains generally handle that speed well. In an animal evolved to handle faster flight, they will already have eyes with a wide field of view, and brains calibrated for that kind of speed. They may not need artificial rules to avoid collision.