I saw the title and thought, "Oh, that sounds a lot like Dungeon World."
And guess what? Ironsworn is
pretty heavily based on the PbtA structure. It alters the resolution mechanic (1d6+MOD vs two separate 1d10 rolls, as opposed to 2d6+MOD vs fixed difficulty ranges), but the Moves are very obviously PbtA moves with modifications.
So yeah, I have no problem with doing this, and I think it is a huge improvement over the way D&D usually handles information-gathering rolls. Because lies or "you don't know" etc. just encourage metagame behavior from players--or, worse, encourages them to constantly ask for rolls
all the time because there's no consequences.
Instead of changing the world on the fly or asking the player to pretend not to know the information supplied is false, it might be easier to just have the failed check effectively impart disadvantage to some future roll (ability check, attack roll, saving throw) that the DM can apply when appropriate. It represents perhaps some level of misapprehension or misinformation that comes back to bite the character in the future when it comes to dealing with whatever they failed to recall lore about. All the DM would need do is keep a tally of how many of those disadvantages accumulate.
Why call it "changing the world on the fly"?
It is revealing something the party did not know was true before, but does know is true now. This sort of thing happens
constantly in ordinary play. If you were already doing just fine with revealing new information as the party goes despite not having the entire campaign world perfectly nailed down to millimeter precision from before session 1, I don't see how this could cause any conflicts that you wouldn't have had from just ordinary play anyway. That is, we're all human, we forget things, we change our minds, we accidentally leave in contradictions because we didn't think things through perfectly, etc.
"Changing the world on the fly" makes it sound like the world is some airy nothing, mere play-dough that reshapes itself for every player action. "Revealing the world as it is discovered" clearly indicates that nothing in the world is
changing; it always was whatever we learn, we just learned that
by playing, rather than by someone plotting it in advance and waiting for the moment it is revealed. Some amount of preparation is of course good and useful, but leaving room for actually discovering answers, rather than always having every answer long before any questions could be asked, leads to a much richer experience for everyone involved. The two--planned-in-advance and discovered-through-play--enrich one another. As seen here, where disadvantageous knowledge makes knowledge checks much more interesting and even risky, while exclusive reliance on pre-planned knowledge leads to various issues.