Right but to demonstrate that you lied about X they have to demonstrate X. So by the time you're deporting someone for the lie you could just as easily have deported them for the thing itself.

You're making assumptions the thing they lied about and the thing they are being deported for are the same, and quite often the thing you're actually being deported for is not a reason to deport anyone at all.

You come to the US and make a social media post saying Trump is a big fat dummy head.

You get deported for lying about being in a terrorist organization.