The amount of radiation is well-known. The total amount of exposure expected for a 2.5 years manned mission is equivalent of about few hundred years here on Earth. It's the effect on human body that is not well-known i.e. how much is the increase in the risk of dying from cancer. The estimates vary widely and there is no good way to test it. In the end some sort of radiation protection will have to devised before any manned mission to account for the potential severe solar storm which we already know is lethal within the magnitude of hours. I admit NASA is very much conservative on this front. Actually they are very conservative on most fronts. But the risk is real and not some figment of imagination.
As for a type of protection, you'd be correct in that lead would be right out, due to mass.
Would it perhaps be possible for a ship to carry a device to replicate the effect of a planet's magnetosphere? I'll admit right off that I don't know enough geology to know how the Earth create's it's mangentosphere or if it's possible to replicate on a small scale, but something like that could reduce the amount of radiation absorbed by the craft and crew...