I have 2 presses that are identical to the press in your link, my presses are not suspect but they do not have the leverage of a Rock Chucker. Most of my case sizing does not require anything special when it comes to lube. I have a lube that is not a case lube, the label is long gone, I call the lube 'no name'.
I do not lube the neck and I avoid lubing the shoulder. When sizing a case I start by adjusting the die overtime. When I start sizing I make sure the case gets sized.
A case has an ability to resist sizing, there is a chance the case has a greater ability to resist sizing than the press can overcome. Back to checking to see if the press won or the case won. If the case wins the die does not make it down to the shell holder, for me it is a matter of measuring the gap between the bottom of the die and top of the shell holder.
When the going gets difficult I go to the 'no-name lube' especially when case forming. I have 16 forming dies, there are times case forming gets tuff. Again, the lube makes the difference.
I purchased a new rifle from Winchester with the ugliest chamber I have ever seen. The length from the shoulder to the bolt face was too long, the diameter of the case was too large and the chamber was gouged. I went to the range with two Winchester 300 Win. Mags. The Winchester shot patterns like a shot gun and the Weatherby shot one hole groups when shooting the same ammo.
The cases shot in the Winchester could not be sized in a Winchester 300 Winchester Mag dies. I sent the Winchester back to Winchester, we had words. I wanted a rifle with a chamber that matched my dies or I wanted Winchester to make me a set of dies that matched their chamber.
F. Guffey