Your height sensors will go out of calibration causing one side or front or rear to be higher than the other in order to fix this you will have to take it to the dealership yes them, and get it re calibrated from what i herd it is a pretty pricey job.

jack the car up and remove the wheels
remove the swaybar links (2x)
unbolt the sway bar busings (2x - 4x)
Replace worn parts with new parts and installation is reverse of removal

Me being a mechanic for 35 years, I have always shut the switch off in a Ford air suspension vehicle before lifting the vehicle, however, if this situation which you describe - forgetting to shut the air bags off before raising the vehicle were a cause of failure, I would have heard of at least one case of this in my years in the business and I have not heard of even one case of this cause and effect. When the switch is turned you are simply turning off the compressor. It does not change the anything about the condition of or the amount of air already in the air springs as the vehicle is lifted. Turning the switch off prior to lifting the vehicle is done so the bags do not deflate while the vehicle is on the lift should the key be turned on while it is on the lift. If the bags were to deflate while on the lift, after the vehicle is lowered it will sit too low but will not damage the air bags. It is my personal opinion that sometimes the air springs in your Town Car or any Town Car for that matter, when the springs are old the rubber dries out and gets cracking and porosity where the rubber part of the bag makes contact and rolls against the plastic spring frame and they leak. What would make more logical sense is that sometimes just the action of raising the vehicle up in the air (switch for suspension on or off) allows the air bags to extend to their full reach because the rear axle housing hangs with the car in the air. This allows the bags to unroll to a place that will only occur with the vehicle in the air. An air spring in good condition would handle this, however, and old 10 years or more air spring might begin to leak from that point on. This I have had happen to me in my own shop once some years ago. The customer put me in the same position you have put that service advisor in. I showed him the dry cracked air springs, I sprayed windex on the bags with it on the lift and the visual was hard to dismiss. The air bags were shot. Dried out like an old tire and foaming at the porous cracking at the folds of the bag. I did not make that happen by me servicing the vehicle. Anyone who raised this car would become blamed for the car being low to the ground the next day.

Yes, you have to get it scanned or bring it to mechanic to get it "CHECKED".

Thats the only solution chief for now, we wont know the answer to the light without examining it.

If the front of the car is at normal height I would suspect the ride height sensors to be bad they are located at the bottom of the air spring assembly. Their is a bleeder valve like a tire valve on the pump its self, just push the middle in and the air should come out if it doesn't try it when the pump is running is should help. Some times you have to play with it buy turning you car on and off, if you are referring to air ride using mcpherson air struts, the pump switch is located in the driver side of the trunk, turn it on. if it doesnt "level" to normal height then check your level sensors. in either case, the default is 25 psi, and releasing the valve at the pump wont solve the problem.

It sounds like your air compressor is over heating meaning you need to replace it. you can go to the junk yard and find one for a third of the price of a new one, if you plan on keeping the car go buy a new one with a warranty. Depending on what you have to remove to get to it it will take about a half hour to R&R it.
GOOD LUCK !!!

Check rubber gromlets to sway bar these are notories for rotting out!

Check your ball joints. Push down on either side of a car and see where the noise comes from...