It's exactly the same principle as making a boat out of steel - lumps of steel sink, a large enough hollow steel container floats because the total density of the container and air inside it is less than that of water.
Similarly, you make a large enough container out of lead and fill it with a gas less dense than air (e.g. helium, hydrogen, or possibly hot air) and it will rise into the air. But it has to be thin lead and a very big balloon to work. Just had a look at the
Youtube video of this, they said the lead weighed 11kg, so the air it displaced had to have a volume of at least 14 or so cubic metres. In fact it was much more since they didn't use pure helium. Someone has done some detailed calculation
here , and in order to make this work they've used lead about 0.016mm thick - that's about a third the thickness of cheap clingfilm, if you want a comparison. It probably wouldn't stop any radiation, except possibly "soft" alpha particles. Certainly not x-rays and presumably not x-ray vision.
