the friction plate was installed off center
The friction plate is loose when you pull the clutch in and would center itself. And if it were installed off center then you'd never be able to get the transmission back on.
Are you certain that it is a BMW clutch plate? Maybe they used something aftermarket. Or it was just a bad clutch plate. :dunno
BMW clutch plate:
(http://i82.photobucket.com/albums/j246/smithduck/k75f/k75f_034.jpg)
You can put as much lube on the splines as you want. Just make sure that you only put it on the trans input splines and that there isn't any on the front of the trans input shaft. Any that gets pushed out of the rear will be pushed out past the collar on the clutch plate and spin harmlessly off onto the wall of the bellhousing.
(http://i82.photobucket.com/albums/j246/smithduck/k75f/k75f_040.jpg)