When lead acts as a poison, it can do so by either replacing another ion (such as zinc) in the active site of an enzyme or reacting with cysteine side chains to form covalent bonds. which of these is irreversible and why?

The second possibility is the irreversible one: forming covalent bonds. Covalent bonds are formed when two atoms share electron pairs, resulting in full outer electron shells and thus greater atomic stability. Since covalent bonds can be so strong, it can become impossible to separate these atoms (thus making these bonds irreversible). 

This movement is also referred to as  glacial plucking