Getting back to the original question, when I was still casting my own bullets, I gave up on my old Lyman lube sizer years ago.
I bought what is probably the best system there is for sizing and lubing bullets, the Star Lube-Sizer made by Magma. It is not cheap, more expensive than a Lyman or RCBS lubesizer, but in my humble opinion it is much better. With the RCBS or the Lyman, you need a top punch fitted to the ogive of the bullet. Instead, the Star runs the bullets through the die upside down. You don't raise the bullet up to remove it, you let the next bullet shove the first one out of the bottom of the die while each new bullet is run through.
It used to take me a long time to size and lube with my old RCBS lubesizer because of having to raise each bullet up to remove it. As my old pard Lou Graham used to say, the Star just poops them out one after the next. You just catch each one as it poops out the bottom of the die.
The Star is expensive, and so are the dies for it. But when I was casting my own bullets I could size and lube a few hundred bullets in an hour or so.
As you can see in this photo I use sticks of SPG lube with my Star Lube-Sizer

Regarding pan lubing, I did that many years ago with regular hard cast bullets for Smokeless powder. Never did it again once I discovered the Big Lube bullets and my Star Lube-Sizer.
https://www.magmaengineering.com/magma-star-lube-sizer/