Recent experimental progress has enabled the controlled generation and confinement of excitons in low-dimensional semiconductor systems, highlighting their potential for excitonic transport and optoelectronic functionalities. In this context, understanding the quantum transport of excitons and their interaction with phonons is crucial for describing energy relaxation, coherence, and scattering processes. However, a fully quantum-mechanical description of exciton transport including phonon interactions remains missing. In this contribution, we then derive an analytical expression for the exciton-phonon interaction self-energy within the Fr"ohlich framework and incorporate it into a nonequilibrium Green’’s function (NEGF) transport approach. We apply our model to a lateral WSe_{2}-MoSe_{2} heterostructure where a diode-like exciton transport has been experimentally reported. Our simulations reproduce the rectification behavior and also reveal the dual role of phonon scattering. Depending on the phonon temperature, phonons can either reduce the exciton current through relaxation or assist transport by enabling excitons to overcome the heterostructure potential barrier. This highlights phonon populations as a natural knob to tune exciton transport via temperature.