I have never tried white lightning, but since the recent negative reports about it in lubing knives, I have no desire to.
Tuf-Glide, the active ingredient in Tuf-Cloth, is a thin film corrosion inhibitor. It has minimal lubrication abilities, inadequate for the high stress pivot pin area. There is a Sentry product which is good for this, Hi-Slip Grease. This works very well, but is MoS2 based, so is black and gets on everything.
I just used some Chris Reeve fluorinated (i.e. PTFE or Teflon containing) grease on a new, stiff Buck 110, and it slicked up the knife very well. It has the advantage of being white, so won't show on your hands or clothes. Shooter's Choice makes a good grease, which comes in a plastic syringe as does the Chris Reeve product, but it is red in color.
Another alternative is a PTFE containing oil, such as the one put out by Dillon. This has worked very well for me. Break-Free is another PTFE / oil combo, and some people have had good results with it. I suspect that it has been reformulated, as it was tested by Gun Tests about 6-8 years ago, and showed absolutely no decrease in the friction between two steel plates under load.
Bottom line: if staining is not a problem, go with the Hi Slip Grease; MoS2 plates the metal parts and cannot be beat (I use it on the slide rails of my 1911s ). If staining is a problem, go with Chris Reeve's PTFE/grease or a PTFE/oil combo. The former will probably give better lubrication under high stress.
Hope this helps, Walt