The lubes I remember using are 3-in-one, WD-40, wax type bicycle lube, Quick Release and Nano-oil. I say this because there are lots of other great lube products available but these are the only ones I remember using.
My BF (GB) has always been an extremely smooth, easy to open knife. The blade has always been centered in the handle when closed. I forced a patina on the blade a few days ago. When I got it back together and after I adjusted the pivot to my liking I noticed the blade was no longer centered when closed. I tried a couple of thing but found nothing satisfactory. I could center the blade by tightening the pivot but that made the blade too stiff for my liking. I then figured the patina was causing more friction between the blade tang and washers. I used to have the pivot just as tight but now the blade was stiff. So I put loc-tite on the screws to maintain the "too-tight" adjustment with the blade centered and used Quick Release on the pivot. Of the lubes listed above QR is the best right next to Nano-oil. I love QR as a lube. In this case it made the knife perfectly smooth. I still needed to loosen the pivot adjustment to get the easy motion I wanted. This morning the blade was still centered because of the loc-tite. Prior to the loc-tite I could adjust it but the screws would back out (I assume) enough for the blade to go off-center again. I applied Nano-oil 10w and it helped. It did take a long time though. I had to wait almost 5 seconds. Now the knife is as smooth as ever, the blade is centered when closed and I am happy. I don't mind a blade being off-center very much. In fact, I don't care at all about that. But,,, knowing something isn't as perfect as it used to be or should be does bug me.
One huge claim of Nano-oil is that it works better when moving parts are under a huge amount of pressure and/or repeated very fast movement. I think this refers to big machinery and rapid fire firearms. All I can testify about is the fact that I can tighten folding knife pivots tighter when using Nano-oil than when using any other lube I have tried. I don't remember the knives but this isn't the first time I've been able to reduce or eliminate unwanted blade play by using Nano-oil.
Since I already have QR and like it I have been using it and saving the Nano-oil for times when the QR didn't quite "do it" on the job. In fact, I had been using QR on the GB for a year or so prior to forcing the patina. When I first got Nano oil I used it on everything that had a moving part. Knives, tools, elbows, etc. Now I only have about 1/4 tube left. This will probably last me another year or three but just to be sure I ordered another tube of the 10w.
I also have some 5w. This weight is miraculous for getting into REALLY tight places. It then dries leaving the lubrication but not the mess. If you apply too much at first it is a bit messy but wipe off any excess and what stays in the pivot stays. The 5w has also made it very easy to break free some rusted bolts in 10 seconds that normally would need to soak in WD-40 overnight. The 5w has about the thickness of water and soaks into the corrosion almost immediately. Save a lot of time and work IMO.