Scalable plasmonic nanostructures are reliably created by controlled drying of a colloidal suspension on prefabricated templates. More complex structures such as hexagonal, Lieb, honeycomb, or Kagome lattices are required to develop specific band structures. Laser inference lithography (LIL) combined with template-assisted self-assembly (TASA) offers fabricating nanostructures reliably with high precision over large areas. Less well-known is that more complex 2D lattice geometries are possible with phase-engineered interference lithography (PEIL). Using optical design and electromagnetic simulations, we numerically propose the potential of PEIL towards realizing complex structures of various periodicities. We present the advantages of these structures using dispersion diagrams showing Dirac cones for honeycomb lattices, which are known from the electronic band structure of graphene or an optical band gap for Kagome lattices at an oblique angle. Further, based on our simulated optical characterization of the proposed 2D plasmonic gratings supporting surface lattice resonances (SLR), it is possible to achieve an exceptionally small linewidth of 1 nm for hexagonal and honeycomb gratings. Consequently, we discuss the benefits of refractive index sensors, where we found a ten times higher sensitivity for such complex plasmonic lattices. Overall, we propose and estimate the potential of PEIL for colloidal plasmonics to be realized using the conventional TASA method.