Lacquers with airbrushes?

I almost exclusively use lacquers. I have found a terrific source for thinner and the paints as well is your local auto parts store. For the price of 2 small bottles of lacquer thinner at the hobby store, you can purchase a whole gallon of the stuff. I build small (1/87) so the small touch-up bottles of paint do 2 mode3ls for me but you can buy larger quantities.

where would I be able to find and purchase lacquers and the appropriate cleaners for them?

The difference is the carrier in the paint, one being an enamel and the other being a lacquer. Lacquer paints are alright to use in most any airbrush, but care must be taken not to let any lacquer thinner get into O-rings on the airbrush since it will cause them to swell and crack eventually.
This is usually not a problem if you just spray lacquer thinner through the airbrush after a painting session. The problems occur when people try and soak the airbrush body in lacquer thinner. That is when the O-ring becomes damaged.
Lacquer thinner is used for cleanup of lacquer paints and good ventilation is a must as accumulated lacquer fumes can be very dangerous in an enclosed room.

Mike