It depends how much control of mental health issues you want to give to the government. The VT shooter Cho, clearly disturbed, was not picked up by the system and legally bought his guns. But he had crossed the path of the legal and mental health system so that was a screw up.
However, how do you define lunatic? Give everyone who buys a gun a test regime? Clock ever Rx for an antidepressant or other drug used for psychiatric condition? Ban diabetics from having guns as if not controlled they can act irrationally. A large proportion of the population have taken antidepressants for example.
No current NICS check deals with that and do we want that? Want to ban something - ban alcohol as a tremendous number of firearms crimes are under the influence as compared to the number committed by those with diagnosable mental illness.
If the issue is unchecked private sales - then the gun show is just seen as an easy venue for such. Having mandated NICS for private sales at a show isn't a real big deal but it won't touch the crime rate. A friend of mine sold his Sigma in the parking lot - personally, I wouldn't sell a gun to an unknown. But do we have NICS cops in the parking lot.
The core issue is banning private sales. Do we want to go there? It would only slow down legal private sales - ya think?
About shotguns - my skeet teacher was a hard core CHL type but I see the point for the moneyed classes - class warfare - O/U shotguns to the barricade!