Got as far as taking the trans out to replace oil.. turns out it's not a K46, but a CVT trans (model unknown). As far as I can see, no option to add any fluids/lubrication.
Mower seems to work ok when the freewheeling lever works correctly (positivity locks in and out, both positions). But when issues occur, that lever will be in one position only, and won't engage the other position. So far that lever regains locking into both positions after a number of hours of no use (cool down?).