Please excuse what follows if it turns out to be a dull comment (I've never used, let alone owned, an LX)
Presuming that the film speed and aperture remain constant, it's only the shutterspeed that is varied by the camera. 6 seconds, when compared to 4, is only half a stop - so the LX is only really making a very minor adjustment when it automatically exposes for you. I wouldn't really consider this to be 'excessive' variation from the manually metered scene . . . but it does hint at some sort of inconsistency in the operation of the metering of the camera.
Do you know how this manifests itself on the developed film / prints yet, or have you not had the opportunity to get the processing done yet?
The battery drain would leave me a little more concerned - (bear in mind that I don't even know how the meter on the LX is activated!)
Battery drain is only something I've experienced (very limited experience!) with a P30 . . . . . . which has been left switched on . . . . . . . . more than once - hardly a camera problem in my case - just an issue with the idiot using it
(something that limited use of a K1000 has never revealed as a problem - I seem paranoid about getting the cap back on if using that). It took over a week of being left 'on' for the P30 to kill its battery - so not that long really.