"and lead itself is radioactive anyways"

Um, I guess in that there are naturally occurring isotopes of lead that are unstable. But those are very rare and can be removed. By this standard, the chips themselves are radioactive since they are made of silicon. By this standard, you, everything you eat, every plant and animal is radioactive since there are trace isotopes of carbon that are radioactive (that's how carbon dating works). And sunlight is very radioactive by this standard.

However, the materials we actually use in chips is highly processed and radioactive isotopes will likely be removed if a centrifuge was used in any step in concentration process. Likewise the lead used in a space shield will probably have similar processing of the material

"Also, lead is extremely dense."

This is the real reason lead isn't used. There are plenty of other elements that shield ionizing radiation quite well and are less dense. However, they are also more expensive than lead which is why we use lead on earth for shielding (its cheap) and use something else in space (where density is more important than price).