Sounds like you're all good then...that all sounds very much in line with a good plan IMO.
Another simple analogy for breaker sizes having nothing to do with the capacity of what we plug into the circuit:
Your entire house is probably 12 gauge wire with 20 amp breakers, or maybe 14 gauge wire with 15 amp breakers...right? This is typical in most localities. Yet we'll plug in a TV wired with 18 gauge lamp wire, that will only draw maybe 3 or 6 amps or whatever into these 20/15 amp circuits...and this is not a safety concern...nor is it an issue with a drastically oversized breaker protecting the TV that pulls much lower amps. Right? This is why there is nothing wrong with using a 40 amp breaker...or even a 200 amp breaker...on your 20 amp welder. As long as the house wiring in the wall is sized appropriately for the breaker. That's the ONLY thing the breaker must either match or undersize...the wiring installed in the wall.
Lincoln is suggesting a 40 amp breaker likely as a convenience. It's guaranteed 100% to never pop. But once you get past the receptacle in the wall, size of breaker and size of wiring is essentially meaningless because only one of two things can happen: 1. You plug something smaller in, it never uses the capacity provided (typical). or 2. You plug something bigger in (oops or stupid), and the breaker trips in order to protect the house wiring from overheating and saves your family.
I'm speculating that the instructions in the Lincoln welder were not referring to house wiring at all, but instead to with input conductor wiring (the cord attached to the welder itself). I know my Hobart welder came with clear instructions and sizing limits (gauge and length) of how to size a replacement cord...and you may have been mistaking these instructions provided with your Lincoln for actual house wiring instructions, which I would find highly irregular...Lincoln should simply refer you to your locality's wiring code for home wiring, and I suspect would not print any type of home wiring advice in their manuals at all.
