Title: Thresholded Lexicographic Ordered Multi-Objective Reinforcement Learning. Abstract: Lexicographic multi-objective problems, which impose  a  lexicographic importance order over the objectives, arise in many real-life scenarios. Existing Reinforcement Learning work  directly addressing lexicographic tasks has been scarce. The few proposed approaches were all noted to be heuristics without theoretical guarantees as the Bellman equation is not applicable to them. Additionally, the practical applicability of these prior approaches also  suffers from various issues such as not being able to reach the goal state.  While some of these issues have been known before, in this work we investigate further shortcomings, and propose fixes for improving practical performance in many cases. We also present a  policy optimization approach using our Lexicographic Projection Optimization (LPO) algorithm that has the potential to address these theoretical and practical concerns. Finally, we demonstrate our proposed algorithms on benchmark problems.