So if he lied on his 4473, then he did NOT purchase the guns legally.
He's probably related to Hunter Biden.
Question 11.f. Have you ever been adjudicated mentally defective (which includes a determination by a court, board, commission, or other lawful authority that you are a danger to yourself or to others or are incompetent to manage your own affairs) OR have you ever been committed to a mental institution?
The question reflects it’s date origin, which was 1968 when the 4473 was introduced. Society has changed considerably. Mental institutions closed, and the mentally ill are no longer funneled through the court system. Almost no one meets the criteria, no matter how crazy they are.
And even if they met the requirements, I doubt there is an existing mechanism for getting that information in a database similar to the NICS where the background check is done.