You might want to look at the RCBS progressive machine. It has 5 stations, but is the only one I know of that uses the first station for a lube die, with the sizing die at the second station. Case lube is simply not cleaned off until the round is fully assembled. At that point a rag with a little mineral spirits will do well enough.
A second consideration: though you have to trim once before using it, RCBS also makes and X-die in .22 Hornet. This will full-length resize, but controls case growth so the progressive process does not need to be interrupted by removing the the cases to trim them after sizing, as is normally done.
If you are going for neck sizing, more issues are involved, as you have the trimming come back into play, though not every load cycle, as a rule, and the Lee Collet die doesn't seem to grow necks at all. However, you eventually have to put even neck sized cases through a FL sizer because they start fitting the chamber too tightly. It may be possible to use the X-die with a reduced expander and set it up for shoulder bumping only, rather than sizing all the way back. Many feel this produces better accuracy than neck sizing alone will do, as it slightly narrows the case to give it room to self-center in the chamber before firing. You would then expand the case mouth separately with a Lyman M type profile type die at the expander/powder feed position. That helps bullets go into the case more straight anyway. I'd have to play with the setup to see how to make that happen as I envision it, but you'll probably have to consider at least a bit of customizing of the die setup to accomplish this.
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