A "zero tolerance" policy and a "lifetime ban" are completely separate things.
"Zero tolerance" is a type of enforcement--true "zero tolerance" means that if you break the rule, you will receive the punishment, no exceptions. "Lifetime ban" is a definition of a type punishment that is available for those who punish those who violate the policy.
A zero-tolerance policy can have many levels of punishment, based on elements such as specific offense (a "zero-tolerance" rule against possessing weapons could still have different levels of punishment for carrying a knife vs. carrying a suitcase packed with explosives) or repeat offenses. "Zero tolerance" and "lifetime ban" aren't synonyms.
"Zero tolerance" is a type of enforcement--true "zero tolerance" means that if you break the rule, you will receive the punishment, no exceptions. "Lifetime ban" is a definition of a type punishment that is available for those who punish those who violate the policy.
A zero-tolerance policy can have many levels of punishment, based on elements such as specific offense (a "zero-tolerance" rule against possessing weapons could still have different levels of punishment for carrying a knife vs. carrying a suitcase packed with explosives) or repeat offenses. "Zero tolerance" and "lifetime ban" aren't synonyms.