While I am not an authority, this is what I recently learned when I was in your position, seeking an LX for the first time.
READ THIS and specifically THIS.
Since the body is specially sealed against dust, whenever the body is opened to service internals (as part of the general CLA, such as timing the shutter) those dust seals must be replaced. The stock of seals kits is diminishing as LX'es are refreshed and the additional work accounts for much of the premium price for an LX standard service.
The good news is you'll get 10 or so years out of your camera, at least.
You might consider purchasing an already-serviced LX instead. PM me if you choose to pursue that option.