There's a third way to approach lubing, sizing, and cleaning, and I have been employing it for quite some time with good results:
First, when you get home from the range rinse the fired cases in plain water and set them aside to dry. The whole purpose of this step is to remove dirt, sand, and grit that could harm the sizing die. This is all the case prep that many of the guys at my range ever do; their cases aren't pretty, but they seem to work just fine.
Next, size and deprime. I tend to lightly lube even handgun cases resized with carbide...just a little Imperial on your fingers makes the process smoother and easier.
Finally, tumble. Besides cleaning the cases, you're now removing the lube. I wet tumble, but dry tumbling with corncob and/or shells also does the trick.
After experimenting with all of the processes listed above, I finally settled on this one, and I am quite happy with it.