  The interplay of spin and lattice fluctuations in two-dimensional magnets
without inversion symmetry is investigated. We find a general form for the
magnetoelastic coupling between magnons and existing chiral phonons based on
the symmetries of the crystalline lattice. We show that in hexagonal lattices,
the coupling of magnons and chiral phonons derives from an anisotropic exchange
spin model containing topological phases of magnons. Using the
Heisenberg-Kitaev-$\Gamma$ model, we show how magnon-polaron edge states with
circular polarization arise from this interaction. Our findings exploit the
polarization degrees of freedom in spin-lattice systems, thus setting the
ground for the transfer of angular momentum between chiral phonons and magnons.
