So I got this cheap live center on eBay, and have some questions

[projectnut]

My take as well. I just don't use a live center when I need near zero runout- which isn't often enough to justify the hundreds of dollars for one.
I use a dead center, plenty of STP lube on the part/center and turn at as slow an rpm as I can to get the results needed.

White lead used to be the preferred lubricant for dead centers. When it was taken off the market I searched for months for a replacement.

On the recommendations of several from another professional board I switched to Honda Assembly Lube. It was originally developed to be a parts lubricant when assembling motorcycle engines. I’ve used it for many years. I think it works better than white lead and isn’t hazardous to your health, except possibly for those who live in California