Should I use cheap or expensive lubricant?
There are actually some organizations that have tested various chain lubricants against each other. However, some caveats. The easiest thing to test in the laboratory is drivetrain friction. The chain's durability to contamination is harder to test, although one person has done this.

The research is described in this Cyclingtips article. One caveat is that it's aimed mainly at performance-oriented cyclists. Friction Facts did the drivetrain friction test, and found that the worst tested lubricant (White Lightning Epic Ride) cost you about 3 watts of drivetrain friction versus a good lubricant, e.g. NFS, Rock-n-Roll Absolute Dry, two Finish Line products, or even Mobil1 5W-20 motor oil.

3 watts is not a lot of power, though. It is unlikely to cost you a significant placing in an amateur race. I suspect that the minimum difference an average cyclist can perceive is bigger than 3W (albeit I know of no studies of this question).

You also might want to consider durability. For example, some lubricants attract less dirt than others. White Lightning claims that some of its lubricants are self-cleaning, and I got suckered by this when I was a newer rider, but it's very likely untrue in White Lightning's case. Dirt on a chain works like a grinding paste, which is why it's better to keep your chain clean (which, admittedly, a lot of cyclists don't do). Zero Friction Cycling's test reported the estimated running costs of each lube under the test protocol, which involved contaminating the chain gradually and replacing it once it hit a specified amount of wear.

Your question as asked in the title can't be answered exactly. It's more complicated than that. Also, I don't know that the inexpensive oil you report using on your other question was tested for wear; the friction test does report Mobil motor oil, but I'm not sure how your oil compares to this. I guess we can definitely say that people should not use White Lightning Epic, unless White Lightning is giving you chains and cassettes for free. Most people should probably also stay away from Muc Off Nanotube or Hydrodynamic lubricants, since they seem to wear fast and are very expensive. That said, it's probably safe to assume that they're very low friction lubricants (they don't appear to have been specifically tested for friction); if you compete in the Tour de France, then I believe your equipment sponsor will take care of the chains, so you could and maybe you even should use those lubricants. (Alternatively, if you are a competitive road racer, you could also just leave this question to the directeur sportif and the mechanics.)

The article did report that one of the testers recommended not using oil-based lubricants. They generally seem to have higher friction, and their viscosity attracts grit, which damages the chain (but note that the same person said this might not apply in harsh off-road conditions). So, you may be better served by going to a dry lubricant. They recommended one particular lube, which I also use. But other good ones are probably more widely available. We don't discuss product recommendations here, and discussing specific products (aside from the ones above!) isn't necessary to answer the question, so I must recommend you read the article and do your own research. If you have two bikes, you could try out a dry lube on one and see if you can keep the chain cleaner with it.

Aside from that, I have to wonder if most lubricants (aside from White Lightning Epic) would perform adequately if you kept the chain clean. The method you described in your other question doesn't really clean inside the rollers very much. On-bike chain cleaning devices aren't very expensive, and they will brush inside the chain. This should help you get the chain cleaner.