The novel two-dimensional honeycomb layered Cu3LiRu2O6 exhibits Pauli-like paramagnetic and Mott variable range hopping semiconduction behaviors, which contradict the large specific-heat Sommerfeld coefficient for metals, and indicate a possible spin-excitation induced nonmetallic metal. This nonmetallic feature can be significantly suppressed by pressure toward producing a bad-metal state, as reflected by the temperature-dependent resistivity response up to 35 GPa.