And yeah, I was terrified. It was a mistake to talk to them in the first place.
They got in my door by telling me they wanted my opinion on some activity they felt is a threat to a visiting president then things took a fast turn asking me about my research and contacts.
FBI is 100% allowed to lie to you but if you lie back to them they own you. They also like to catch you unprepared and off guard. Don't fall for it.
Say something like:
"I'm sorry this is not a topic I feel well prepared to talk about right now. If you have a court order I will honor it but even then I am going to need time to collect my thoughts and ensure I am speaking accurately. I'll walk you out"
Then get a lawyer to coach you on what you can and can't say. If they catch you in a lie even by accident they can -force- you to be an informant.