> Congress isn't above lying about this.
Agreed. I also note that the Intelligence Agencies aren't above lying to Congress (whether behind closed doors or in public hearings), to the DoJ, the Supreme Court, the President, or anyone else for that matter.
> Also... "prohibited"? By whom?
Uh, actually prohibited by long-standing Federal law? USC Title 18, Section 793, and Section 798 totally apply here. Congressmen are NOT immune from prosecution that stems from their disclosure of classified information that they receive firsthand.[0] What's more, the Speech or Debate clause only protects Congressmen from arrest and detention while performing their official duties. It doesn't shield Congressmen from prosecution stemming from illegal acts performed while acting as Congressmen.
So, no, Federal agencies can't prevent[1] Congressmen from revealing directly-disclosed-to-the-congressman classified information on the debate floor. But then, a Congressman can't protect himself from prosecution, fines, and jail time after the big reveal.
[0] Remember that the Pentagon Papers were sent to a Congressman by a newspaper. Generally speaking, disclosure of classified information that's in the public interest by a person who is not under an obligation to control access to said information is a protected activity, as is disclosure of classified info by the press.
[1] Though, they can directly discourage it by limiting cooperation with Committees and access to personnel. This would clearly be a roadblock, rather than a permanent obstruction, but it would probably serve as a permanent obstruction to dispassionate Congressmen.