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Honeycomb systems containing ions with a large spin orbit coupling and a nominally non-magnetic single-ion state have been proposed to host novel magnetic ground states [Phys. Rev. Lett. 111, 197201 (2013)]. Our susceptibility data on Cu₃LiRu₂O₆ (containing Ru⁴⁺ (4d⁴)) exhibit a broad maximum around 300 K and a Curie-Weiss fit of the data above 300 K yields an effective moment of 2.42 μ_B and a Curie-Weiss temperature θ_CW = -222 K. There is no evidence of magnetic order down to 300 mK in heat capacity which varies as T² at low-T.  The finite T-independent ⁷Li NMR shift down to 2 K indicates a finite spin susceptibility and hence a magnetic state. The ⁷Li NMR spin lattice relaxation rate shows no evidence of magnetic order and varies linearly with temperature at low-T which is reminiscent of a Fermi liquid. Our results point towards the observation of excitonic magnetism in a d⁴ system together with the stabilisation of a spin liquid state at low-T.