If you don't have the manual for the LX, visit this site
http://www.butkus.org/chinon/ where you will find one you can download. And send Brother Butkus a little money so he can continue his valuable work!
Now. The LX has an exposure compensation dial concentric with the rewind crank. Check that it is on "0". If it is miss set that could be the problem. Otherwise follow the advice of Fred Aspen above. If the offset is linear you could use the compensation dial to accommodate it and set the ASA in the usual fashion. BTW, I assume you know the sunny f16 rule? If not a usable exposure approximation for any camera is to set f16 and the shutter at the reciprocal of the film speed. Thus for ASA 400, set f16 and 1/500 for a sunny day. If the meter indicates close to this all is good. This is what Fred suggested.
The LX is a magnificent machine. It has perhaps the best metering system ever made. If you can deal with the possible cost of a possible CLA - Clean, Lubricate, Adjust - you will find it delightful to use. Watch for a flash which will work with its TTL system. Enjoy!!
I can imagine GRHazelton that OP's problem should be solved from your recomandation. If not we might think on alternate reasons with wrong exposure of LX.
From my point the LX is very reliable. Some state the NikonF3 comming out the nearly same period is much more reliable ! I don't feel that way.
But there are lots problems with Pentax LX today. The main reason isn't its age. It is far behind caused from pricing of Pentax find comfortable for LX.(Nikon F3 was 100 bucks cheaper from the body in comparison to Pentax).
So you may find lots of F3 in good used condition - but Pentax LX is beside the Pentax MX " rare" today.
The reason is very simple. Nikon produced much much more F3 than Pentax was able to sell LX to professional photographers.
That is the problem : the majority of LX was used from professionals. If you might have the idea that isn't correct because : " F3 was THE PROFESSIONAL SYSTEM OF THE EARLY 80th". you are right.
But then you forget : F3 was also "everybodys darling from amatheuric photograpers!
And 85% of F3 photographers wasn't professionals.
The next issue is : you simply are able to notice if a used F3 was professional used (in most cases)
because the type of professional photographers was different to professionals with LX.
(press photograpers)! They gave their F3 cameras no chance to survive the first 3 years...

!
I realy remember just a single situation were I noticed a professional with LX on a press shooting.
His F3 colleagues were laughing about the Pentax LX photographer.
So the percentage of LX cameras bought from amatheuric photograpers was less in comparison to Nikon. The condition of professional used LX cameras is (in most cases) better in comparison to professional used Nikons.
But that is hard to find out with today's Pentax LX : You don't notice much difference via optical inspection.(professional used or amatheuric used).
Some amatheuric LX are looking more worst than professional used ones.
That is also caused from its age. (Pentax LX came out 1981) the last ones were sold 1997 !
(2000 this Y2k edition was presented) :
If you spend that money a Y2K cost today you definitivly will see no technical problems for many many years.
The same is on a LX in unused condition wich looks like this here :
But this LX (unused) is also rare and still expensive! The produced LX before 1990 are too old -
remember its age > 28 years. A service to change a couple of parts is allways necessary!
( Mirror dampers).
Conclusion : Electronic failures with used LX is possible but much more possible is incorect shutter speed with professional used cameras due to mechanical wear.
If a LX is at the end of its best days the x- synchroner 1/125 is a last option. A service repair is possible for some hundred bucks. And that is the actual danger with cheap LX today.
I saw a used LX 1991 !!!!!! for a cheap pricing ! The LX was much exausted. Today (17 years later )
it should make the intention to buy a good LX to a special kind of challenge - it is a "lottery"

!
Buy the time does anyone own a Y2K ? There is still a guy in Malaysia who deals with Y2K boddies!
with regards