  This paper examines actions of right LCM semigroups by endomorphisms of
C*-algebras that encode an additional structure of the right LCM semigroup. We
define contractive covariant representations for these semigroup dynamical
systems and prove a generalized Stinespring's dilation theorem showing that
these representations can be dilated if and only if the map on the C*-algebra
is unital and completely positive. This generalizes earlier results about
dilations of right LCM semigroups of contractions. In addition, we also give
sufficient conditions under which a contractive covariant representation of a
right LCM system can be dilated to an isometric representation of the boundary
quotient.
