When he says "They've been wanting a ballroom for 150 years"

[0rganism]

3. Probably wouldn't want to follow-up with a direct probe, but rather get him to look stupid as he dissembles further

First: it's clear no one really wanted a ballroom there in well over 200 years, as he's obviously lying.
Next: The press doesn't do follow-ups anymore, I guess it's against the law now or something.

If you ask "They who?" F47 goes on the attack and berates you for (a) being a low-IQ individual who knows nothing of the founders' deep abiding love for fortified ballrooms, and (b) contracting with a fake news outlet to ask "gotcha" questions.

I think the optimal approach is to draw him out, get him rolling with a story: "Mr. president, what mysterious trail of deep historical clues led you to uncover your predecessors' long-standing desire for a high-security national ballroom?"

Then he goes surfing in his ocean of bullshit, fabricates a bunch of outrageous slop, and voila comedians have material for the next 3 days. I think that's the best we get from flogging that dead horse.

Press might do better pushing on the corrupt congresscritters who intend to provide public funds for F47's architectural monstrosities.