A small amount of lead - or even a large amount of lead - in an exoskeleton isn't likely to protect against gamma radiation, and even humans are protected against alpha and beta radiation by their skin. A lead exoskeleton would have to be impractically thick and heavy to attenuate high-energy gamma rays.
However, all is not lost. Terrestrial lifeforms are susceptible to radiation due to the sensitivity of DNA to modification by ionising radiation or the ions that it produces as it passes through a cell. However, even in terrestrial life forms, some are far more radioresistant than humans. This assumes that these aliens have DNA as their genetic material, an assumption that is not a certainty by any stretch of the imagination.
These aliens, which the OP desires to be radioresistant, may not use DNA as their genetic material at all. Without going into a lengthy speculation as to what mechanisms of inheritance they may use, it should suffice to say that the various possible mechanisms may be more or less radioresistant than DNA.
Should these aliens use a particularly radioresistant genetic mechanism, the dose of radiation required to cause illness or death may be such that illness or death is caused not primarily by genetic damage, but by destruction of other structures necessary for the processes of life... and these doses of radiation may be so high as to make even the most radioresistant terrestrial lifeforms appear positively fragile to these aliens, potentially on the order of a million Gray, a hundred thousand times that which is acutely lethal to humans, and over thirty times that of the most radioresistant terrestrial lifeforms.
So, these aliens may be highly radioresistant not due to any mechanism by which incoming radiation is attenuated, but rather by their cellular mechanisms being more radioresistant in themselves.