I saw that LX advertised at the auction- bet you got a good deal if you are willing to deal with the minor annoyances. It looked pretty good to me, maybe it just sat outdoors in Alaska without being driven for a a few years before they auctioned it. I bet once you blow the dust out of it and lubricate everything it'll be fine
Is it the stereo factory Lexus or aftermarket?
Does the volume control sound scratchy when you turn it?
Either way: I bet the potentiometer for the volume control is stuck- maybe there is rust or mold growing in there. (I am not kidding about this.) Unless you want to remove the stereo and take it apart, the only thing I can suggest is to squirt some contact cleaner up in there as close as you can get to the volume control, and then work the knob back and forth so that the contact cleaner gets spread around on the surfaces of the pot. Keep squirting and turning until you achieve desired result.
If that does not work, you will probably have to remove the stereo in order to open it up and troubleshoot. If it is the 15 year old factory stereo, it is probably not worth the time and money to repair it -- you would be better off to just replace it with a modern car stereo for $70 or whatever your budget will allow:
http://www.crutchfield.com/p_130150MP/Pioneer-DEH-150MP.html
I am not aware of any noise sensor that automatically controls the volume on the 1998 LX. However, my ride is a Toyota so I don't know for sure. Maybe the Lexus had some kind of automatic volume control, but I don't think so.
Hope this helps.