The FAA doesn't actually require a
permit for outdoor lasers. They do
request that a report is filed 30 days prior (
Advisory Circular 70-1); however, their response is only to object or not object to the operations. This objection is advisory, not binding.
It is also workable with the FAA with laser and bright light operations in the vicinity of an airport so long as measures are taken to prevent interference with an aircraft. For example, spotters could be used to dim lights/lasers when an aircraft is within range, or measures can be taken to ensure that lasers terminate on surfaces so as to not interfere with aircraft in open space.
I believe these "laxed" regulations are just to come in terms with the reality of lighting and lasers. Airports are often near populated areas, and bright lights (and to some extent, lasers), can and will be used within the multi-mile radius that the FAA likes to keep clear of distractions.
So don't be an idiot with your lasers. Shining even a laser pointer into a cockpit is a federal offense. Don't shine your lasers anywhere near an airplane. Lasers get a bad rap as is.
I talked to the guy who did the One Mile Clock art exhibit and they pretty much relied on terminating the beams on the hills around the event. They did not receive a variance or anything from the FAA. I can't remember if they tried.
Speaking of variances. If you're hosting a light show with lasers above class 3b ( > 5mW) you're supposed to acquire a variance from the FDA, who in turn will only issue one if the FAA does not object. The variance is more to protect peoples' eyes by ensuring that lasers are scanned or powered to a level that doesn't cause eye damage. This is separate from the FAA because even laser pointers are still a distraction hazard to pilots at great distances.