I don't recall seeing discussion of this, but my recollection may not be so good. I am not typically a precision reloader. I mostly reload to plink and have fun shooting-up a private cowboy type range on the back lot. I typically shoot a couple hundred rounds per session and that is often black powder cartridge in 45 Colt. So my typical case prep involves cleaning in detergent and water, deprime, tumbling in citric acid water, rinsing, lubing while still wet with Lee case lube spritzed on and mixing onto the brass by hand, then air drying in onion sacks. Other than hand press deprime, its quick and easy.
I used to just wash and then dry the cases before corn cob tumbling, then lubing, drying again, and finally into the progressive press. But cob media residue gave me fits in my dies and prime mechanism. One of the immediate PERKS noticed after changing to use of the Lee Lube on wet clean brass was how easily primers seated when I reloaded. Dang things just slip right in with hardly any effort and nary a tipped/crushed primer. Before, they sorta just crunched in. The lube is now getting in the primer posckets. I wondered if there was a down side to that. If so, I have not found it in about 5 years of doing it this way. Feel free to opine pro or con here.
On a recent batch, I forgot to spritz and mix the lube onto the wet brass before air drying. Realizing the omission after the cases were dry, I just spritzed them and let that dry again. For one thing, the lube made white water spots (duh?) and for another, the primers were crunching in again and it took an effort to seat them. The lube did not effectively get into the pockets that time.
So for easy prime on a progressive press, consider "contaminating" the primer pockets with Lee case lube or similar liquid concoction of your choice.