"I read his paper."
Translation:Eu citesc ziarul său.
In this context, the only difference is that "său" shows the gender of the owned object (masculine), but not of the owner, while "lui" shows the gender of the owner (masculine), but not of the owned object.
In general, "său" is a reflexive pronoun that can be used to refer back to the subject:
"El citește ziarul său." - "He reads his newspaper." (his own - either he made it or simply owns it, but it's not about someone else)
"Lui" could be used to show that there's an owner different than the subject:
"El citește ziarul lui." - "He reads his newspaper. (this could be his own newspaper or of another masculine entity)