It depends on the type of radiation. And the energy level. And the time scale and the type of effects you care about.
It was mentioned up thread that radiation can damage the mechanical structure of a solid. It takes a lot to do that. And lead tends to be kind of a blob, so it takes a lot of damage to make much difference to the properties of lead. But, eventually, you could turn it to a powder.
For beta or alpha, almost anything is good shielding. Alphas can be stopped by just about anything only a few mm. Betas by a few cm. Don't eat that, and you are probably good.
For gamma radiation you need a little more. The 40 inch of lead would probably be good for just about anything you'd see in terms of gamma in space, at least not too far from Earth.
There's lots of other things in space. Solar wind contains protons. Protons probably get stopped by quite thin shielding.
There are also some neutrons. This gets very complicated.
https://en.wikipedia.org/wiki/Isotopes_of_lead
Lead has a bunch of isotopes. It can catch a neutron and go to the next higher isotope. Except for Pb204 that will get you a beta decay to Bismuth. Which probably brings you back to Lead when it catches a neutron. Or Thallium after it decays, which again bounces around with Lead and Bismuth.
But lead can also have a neutron knocked off. The process is sometimes called "spalling" You start with one neutron at 1 MeV and wind up with two neutrons at 0.4 MeV or so. This can actually increase the dose for the person shielding behind it. So, in those cases where there is a neutron source in the radiation, you probably want to not be using lead as your shield.
Which brings us to cosmic rays.
http://explorecuriocity.org/Portals...ackgrounder -Cosmic and Neutron Radiation.pdf
These are very high energy particles. When they hit things they tend to produce showers of radiation. If they go by without that you are generally better off. So having a bunch of shielding is not necessarily the best possible situation. Probably what you want is to have only as much shielding as required for the background. If you try to have a lot of shielding the tendency is for the cosmic rays to kick up a lot of secondary stuff that spoils the benefits.
In our atmosphere, a lot of these shower things happen at high altitude. So the atmosphere is there to catch a lot of it. But some make it to the ground.