Leaving aside the impracticality of large amounts of lead shielding on a spacecraft it would actually be more dangerous because of Brehmsstrahlung - if you don't know what that is google it but if you did know you would never have made the comment about lead shielding in the first place, "bless". Give me a direct link to the NASA comment you keep referring to because I really can't be arsed going through those vids looking for it.
Lead can be necessary to protect against extremely intense bursts of radiation - e.g.an atomic explosion OR an intense solar flare event which I mentioned in my initial post and as I explained there NASA decided to take the risk and do without additional shielding against such high-intensity but rare bursts of radiation. In the case of high-intensity radiation the Brehmsstrahlung effect from using lead or another material with a high atomic number is less dangerous than the high-intensity radiation itself. The Van Allen belts do not contain high-intensity bursts of radiation, they are largely composed of streams of high-energy protons and electrons, the majority of which can be stopped with relatively light shielding - yes, fibre insulation and aluminium sheeting to name two. Sure, some particles will get through but by passing quickly through the parts of the belt where the radiation levels are lower the danger to the astronauts was minimised.