If you're already looking for a Pentax LX, you may not need this guide, but there are a couple things to note:

1) "Sticky Mirror" Syndrome

With age (10-15 years), there are some rubber parts that deteriorate. One of these is the mirror rest: the piece of rubber that the mirror rests on when it is down. It gets gunky and sticky, and after the camera has been sitting a while, the mirror will hesitate a while before it swings up so your shot will be delayed somewhat. This can be prevented by locking up the mirror shortly before taking your first picture.

Since the rubber is deteriorating, the mirror sits a little bit lower than it should; this throws off the precise alignment of the mirror which results in the focus being inaccurate! This is noticable with any wide aperture lens while focused on infinity. Junk stuck on the bottom of the mirror is indicative of a sticky mirror problem.

By the time the rubber bumper has degraded, it is probably also time for a complete CLA. There are also a few internal mechanisms deep within the LX that need some TLC. Expect to pay $150-250 US Dollars for a full CLA.

2) Which version are you buying?

The LX's production run included variations. The earliest versions had a maximum ISO of 1600, which was then updated to 3200. The most visibly noticable update is that of the shutter lock. Versions of the LX with 3200 ISO have two different shutter lock designs! The early design has a shutter lock like the KX, while the later design is quite different. Visit Bojidar Dimitrov's Pentax page for more info.

3) Which Viewfinder & Focus Screen are you getting?

Most LXs will come with an FA-1 or FA-1W viewfinder, but there is another option: the FB-1 base which accepts an FC-1 or FD-1. The FB/FC/FD system is quite valuable, and if you don't want it you can sell it and buy an FA-1 for less.

Ask the seller about the focus screen to make sure you aren't in for a surprise. Do a search for more information about focus screens.

Summary:

If the seller isn't familiar with SLR cameras, assume there is a sticky mirror problem. Asking will probably not be useful as unknowledgable sellers simply won't be able to tell, especially since it requires that the camera to sit around for a while. If the seller specifies a recent CLA (and offers proof), your LX should be good to go for about 15 years.