Lead wouldn't work anyway - it would make things worse actually.

Lead is good for gamma (and X) rays, but very very terrible for cosmic radiation which is protons and neutrons (nucleons).

For those you want water.

It works like this: For photons you want them absorbed, so heavy metals are great.

But it's not possible to absorb nucleons. Instead you want to steal their energy. If you use lead they simply bounce loosing hardly any energy.

Instead you want very light elements - hydrogen especially. Then when they bounce all the energy gets transfered to the hydrogen.

Lead can make things worse because the nucleon can actually fission the lead atom emitting secondary radiation that is even worse than the original.

If you are shielding from electrons you can get Bremsstrahlung radiation if you use lead see: http://en.wikipedia.org/wiki/Bremsstrahlung#Radiation_safety

In summary: Lead for photons, water (or other light materials like wax or plastic) for everything else.

You've written an incredibly interesting comment addressing something I had no idea about, thank you.

You can try it out a bit.

Shoot various size coins at each other and watch how they interact, then try a coin against a wall.

If you have a very slippery surface try making a line of 3 coins (or more if it's super slippery) to bounce against each other.