An Ando-type dilation on right LCM monoids

We establish an Ando-type dilation theorem for a pair of commuting contractions together with a representation of a right LCM monoid via either the Cartesian or the free product. We prove that if each individual contraction together with the monoid representation has $\ast$-regular dilation, then they can be dilated to commuting isometries and an isometric representation of the monoid. This extends an earlier result of Barik and Das.