The Lewis' Mk model is already sort-of in Beast. You would use a
general substitution model to set that up. In addition to the Mk model
you may want to consider using Stochastic Dollo model, which is also
in Beast with examples. I could work with you to help set up the
analysis. It would also be good if we could work together on a short
tutorial on how to set up morphological models in Beast.
Cheers,
Alex