When the electromagnetic modes supported by plasmonic-based cavities interact strongly with molecules located within the cavity, new hybrid states known as plasmon-exciton-polaritons (PEPs) are formed. The properties of PEPs, such as group velocity, effective mass, and lifetime, depend on the dispersive and spectral characteristics of the optical modes underlying the strong coupling. In this work, we focus on lattice modes supported by rectangular arrays of plasmonic nanoparticles known as surface lattice resonances (SLRs). We show that SLRs arising from different in-plane diffraction orders in the lattice can couple with the molecular excitons, leading to PEPs with distinct dispersions and thus different group velocities. These results illustrate the possibility of tailoring the transport of PEPs through the design of lattices of plasmonic particles.