  The superconducting properties and structural parameters, including the
Gr\"uneisen parameter ({\gamma}G), of the BiCh2-based (Ch: S, Se) layered
superconductor LaO0.5F0.5BiS2-xSex were investigated. The superconducting
transition temperature (Tc) increased with increasing Se concentration (x), and
bulk superconductivity was induced by Se substitution. {\gamma}G exhibited a
larger value when x greater than 0.4, where the superconducting properties were
improved. These results suggest that the increase of lattice anharmonicity is
preferable for superconductivity in LaO0.5F0.5BiS2-xSex. The discussion
includes data for related superconductors REO0.5F0.5BiS2 (RE = Pr, Nd), where a
positive correlation between {\gamma}G and Tc is revealed for Se-poor samples.
In addition, specific heat analyses suggest the presence of a low-energy
optical phonon mode for LaO0.5F0.5BiS2-xSex.
