  Engineering non-linear hybrid light-matter states in tailored optical
lattices is a central research strategy for the simulation of complex
Hamiltonians. Excitons in atomically thin crystals are an ideal active medium
for such purposes, since they couple strongly with light and bear the potential
to harness giant non-linearities and interactions while presenting a simple
sample-processing and room temperature operability. We demonstrate lattice
polaritons, based on an open, high-quality optical cavity, with an imprinted
photonic lattice strongly coupled to excitons in a WS$_{2}$ monolayer. We
experimentally observe the emergence of the canonical band-structure of
particles in a one-dimensional lattice at room temperature, and demonstrate
frequency reconfigurability over a spectral window exceeding 12 meV, as well as
the systematic variation of the nearest neighbour coupling, reflected by a
tuneability in the bandwidth of the p-band polaritons by 7 meV. The technology
presented in this work is a critical demonstration towards reconfigurable
photonic emulators operated with non-linear photonic fluids, offering a simple
experimental implementation and working at ambient conditions.
