Power Cord for Power Conditioner

Lamp cord would be fine if the gauge is heavy enough.

Here's one last analogy on this topic which might bring things into better perspective: tires. We all know that putting 4 new tires of the correct size to match your car will adequately allow it to travel from A to B properly. Put bias ply non-radials on a 72 Chevy Impala made from one of the big manufacturers such as Goodyear, Michelin or Firestone and odds are you won't be able to tell which of these brands are on the car based on the car's performance...they are all more than adequate and based on the overall performance capabilities of the vehicle none of them would be considered a particular benefit or liability to the cars' designed abilities. Take a Formula 1 driver and fit his car with those same 3 different brands [of exact same properly-appropriate tires] and the driver will have absolute preferences based on the performance aspects each manufacturer brings to their tires and the ability of the car to wreak every last iota of capability from each one.
Audio systems can be compared similarly; you will not notice as much difference in powercords if you retrofit your 1972 Pioneer receiver with an IEC connector and a decent aftermarket powercord (although I'm convinced it would be an audible improvement) as you would replacing the stock cords of those Mark Levinson monoblocs with an appropriate aftermarket pair befitting the caliber and expense invested in the amps.
If you refuse to believe this and refuse to try it out for yourself, no one is twisting your arm to do so but the audacity so many people show trying to convince others that we couldn't possibly hear a difference is astounding.
Lamp cord of appropriate gauge will not sound anywhere near as good as a properly matched aftermarket powercord from any number of companies such as Shunyata, Synergistic Research, etc. etc. etc....
Don't believe it? Have a nice day enjoying your system with your stock cords.
But please stop preaching about what others can and can not hear.

Lamp cord was considered 18 guage.

Why wouldn't that work on the Levinson's if power cords are all equal?

Because some gear demands better.

And sounds that much better with it.

Lamp cord can be and often is larger than 18 gauge. Your expensive power cord probably has lamp cord inside or equivalent with a fancy wrapper.
As far as preaching what others can hear or not goes it's not my job to prove you can't hear the difference it's your job to prove you can. I have tried it as well as many others with even higher end systems than me and none of us are convinced. When a friend of mine had another friend who is a power cord builder install his PC in his system my friend told the PC manufacturer he could hear an improvement with the new cord. He later told me he really couldn't but didn't want to "tell the emperor he had no clothes"

"As far as preaching what others can hear or not goes it's not my job to prove you can't hear the difference it's your job to prove you can."
Rwwear: You are repeating yourself and I already addressed this EARLIER IN THIS THREAD. I can hear the differences repeatedly as well as many others who took the time to try it (some were very skeptical at first).
This is repeatable... Marakanetz: We could wage 10:1 and you would lose. National TV? No one should be "astounded" about this...thousands of people CAN and DO do this every time they sit down to listen to their systems. The fact that so many can tell is not the mystery here...the fact that so many feel so compelled to insist on DISproving it is the real absurdity.
Listen to what you want to...be happy with stock cords if you can't tell the difference.
But please stop telling everyone else what we must believe..