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Non-Hermitian systems have attracted significant interest because of their intriguing properties, including exceptional points (EPs), where eigenvalues and the corresponding eigenstates coalesce. In particular, quantum systems with EPs exhibit an enhanced sensitivity to external perturbations, which increases with the order of the EP. Therefore, higher-order EPs hold significant potential for advanced sensing applications, but they are challenging to achieve due to stringent symmetry requirements. In this work, we study the dynamics of a generalized lossy waveguide beam splitter with asymmetric coupling by introducing non-reciprocity as a tunable parameter to achieve higher-order EPs even without dissipation. Moreover, we analyze the evolution of NOON-states under activated non-reciprocity, highlighting its impact on quantum systems. Our results open new pathways for realizing higher-order EPs in non-reciprocal open quantum systems.