In this presentation, we will give an overview of Priests material and model-theoretic approach to (naive) paraconsistent set theory. We will highlight several criticisms put forward by Incuravti and Meadows. Then we will outline the problems one encounters in the construction of an algebra-valued model for naive LP Set Theory. Similarly, we will reject this approach due to the weak conditional of LP and to the questionable treatment of identity. But we will propose a possible fix. First, we propose *somehow* to add a class function to the lattice valued model and secondly to discriminate between faithful and unfaithful interpretations of identity. When restricted to faithful interpretations we can show that our *expanded* algebra valued model is indeed a model that validates ZF, the axioms of Naive LP Set Theory and the law of Leibniz. We compare our approach to the model construction of Priest and discuss possible objections.