buzzing noise

my grandma has an 05 lesabre, and it makes a buzzing sound a few seconds after you turn it on, and a few seconds after you turn it off. You can hear it inside and outside. Is this the air suspension?

Probably so. If the sound is coming primarily from the rear area of the car then it is the auto leveling suspension with the rear air shocks. Both Custom and Limited models have it as standard equipment.