If one tells a lie when being deposed, it is perjury.
You assume the interviewer will tell the truth in court, he/she will lie and make up a different reason why they didn't hire you to avoid being fired or covering things up.
You almost have to record them saying it, or having a letter or email where they say it. It is really hard to prove. It comes down to your word against theirs.
They aren't stupid enough to write down "This guy has a mental illness I refuse to hire him" they will make up other reasons to cover up the fact that they don't want to hire a mentally ill person.
I've been through this many times, filed with the EEOC, talked to lawyers, ended up on disability because I couldn't get a job. They never say they rejected you because you are mentally ill. Always "not a good fit", "overqualified", "not a team player", "lack of social skills", whatever they decide to write down even if it is not true.
Lawyers would not take the case because it was hard to prove.
They could just write down "overqualified" or "lacking social skills" or "doesn't get along with others" as reasons and not even mention a mental illness.