Periodic lattices, a central class of phononic structures formed by the spatial repetition of an elementary cell, offer a classical framework for analyzing wave propagation since the early work of Brillouin [1]. Recent developments have highlighted the role of non-local interactions beyond nearest neighbours, which enrich dispersion characteristics and significantly broaden the achievable design space [2]. The Wave Finite Element Method (WFEM), rooted in the pioneering contributions of Mead [3], combines finite-element modelling with periodicity assumptions to compute dispersion curves through an eigenvalue problem. It further enables the study of coupling between distinct lattices by evaluating associated transmission and reflection coefficients. This work investigates the behaviour and optimization of these coefficients when coupling lattices characterized by different non-local interaction geometries. Although WFEM is well suited to the analysis of structures with non-local interactions, we show that a rigorous treatment of non-locality leads to an eigenvalue formulation that departs from the classical WFEM approach. The eigenvalues produced by the two approaches do not coincide, raising questions regarding their respective physical interpretations and the possibility of establishing a consistent relationship between the associated propagation constants. Building on this observation, we propose a general framework for parametrizing dispersion relations in lattices intended to be coupled. We analyse the correlations between the design of non-local phononic structures within the coupling region, the spectral characteristics of the resulting dispersion curves, and the corresponding transmission and reflection responses. Finally, we address the optimization of the reflection coefficient when coupling local and non-local lattices, highlighting conditions under which wave trapping may emerge, in a manner reminiscent of acoustic black holes. REFERENCES [1] L. Brillouin, Wave Propagation in Periodic Structures, Academic Press, New York, 1946. [2] A. Kazemi, K. J. Deshmukh, F. Chen, Y. Liu, B. Deng, H. C. Fu and P. Wang, Drawing dispersion curves: band structure customization via nonlocal phononic crystals, Phys. Rev. Lett., 131(17), 176101, 2023. [3] D. J. Mead, A general theory of harmonic wave propagation in linear periodic systems with multiple coupling, J. Sound Vib., 27(2), 235–260, 1973.