I can tell you that an open minded Romanian can understand this sentence, but this form is never used. It is used the form "Eu citesc ziarul lui". You can use "său" for a sentence with masculine third person "El" like "El citește ziarul său" that can be translated "He reads his own newspaper".
"său" is a reflexive pronoun with no correspondence in English, which usually refers to the subject of the sentence, while "lui" could refer to someone else. In this example, they are perfectly interchangeable, but consider:
El citește ziarul său. - (He is reading his newspaper. The newspaper is his own. Either he owns it or he made it)
El citește ziarul lui. - (He is reading a newspaper, which is either his own, or someone else's who can be referred to as a "he")