I just don’t see how replacing X with X means that we don’t have X.
I think this is the blue dog principle. You replaced something with something else that happens to be "the same", but it really isn't the same any more. Way of the Chameleon (like any Way) replaces following the card's instructions with something else. The "something else" is in this case following modified instructions of the card, but we are still just using a Way, so anything that replaces "following a card's instructions" (Echantress) doesn't see them as the original instructions it can replace.
In the part you're quoting from me I was replying to Hhelibebcnofnena's post that said that Chameleon is different from Lantern because the rules for Way means it doesn't just modify, it first replaces then modifies, whereas Lantern only modifies. So that was me saying that Chameleon modifies just as much as Lantern.
But as I wrote in the end of that post, I definitely see how we could say that Chameleon replaces the ability with something else based on that ability. My point is that then the same applies to Lantern. Conversely, if we somehow say that this is not like "blue dog", that we are still resolving the Action card (just with modifications), then that should apply to Chameleon as well as Lantern. Ultimately, I agree with you and GendoIkari that the first alternative seems more correct.
So what I don't see, and which neither you or GendoIkari mentioned in your last posts, is how Lantern is different from Chameleon. Not as long as they both have the same timing, which I think everybody in this thread has assumed (except Dominionaer, but s/he was basing it on the old version of Lantern). Actually, you (Ingix) also mentioned that Lantern might have a different timing. To me that interpretation doesn't follow at all from how the card is supposed to work. Of course we don't have any FAQ for the new version. But we do know that it triggers every time you play Border Guard and changes what happens when you resolve it. This is exactly how Enchantress and Ways work, so to me it would require some kind of official "errata" to say that it works differently.
tl;dr:
How can Lantern be "the same instructions with a change put in", while Chameleon is "new instructions based on the old instructions" if they both happen at the same time? And what is the basis for saying that they don't happen at the same time?
Because that's how Ways in general work. When a Way is invoked, or Enchantress is in effect, it effectively replaces the text with something new. In the case of Chameleon, the new text is
defined as being similar to the original text, but it's still completely new text. Lantern, on the other hand, is just an amendment to BG
And, actually, I would agree that they happen at the same time, so you can choose the order. But the order isn't relevant for Lantern. Either Lantern modifies Border Guard, then Enchantress/a Way tells you to ignore Border Guard's text (including Lantern's amendment), or Enchantress/a Way happens first, then Lantern has nothing to amend (unless the Way was Chameleon, since Chameleon would leave the text unchanged), and so fails to have any effect. In either case, the result is the same - Lantern doesn't do anything. (Although, by this line of thinking, you could technically use Chameleon to overrule Lantern - I don't know why you'd
want to, but you could theoretically use Chameleon that way)
On the other hand, with Enchantress and Ways, the order
is relevant. Either Enchantress happens first, replacing the card's text with +1 Card +1 Action, then the Way happens, replacing the Enchanted card with whatever the Way does (in the case of Chameleon, "follow the original text, with +card and +coin swapped", and so the original text returns with any necessary amendments), or the Way happens first, replacing the card's text with what the Way does, then Enchantress happens, replacing the Way with +1 Card +1 Action. This is why Ways can replace Enchantress, while Lantern can't do anything about Enchantress