I think it would be okay to assume that the medium is isotropic in my case. Then λ is just a number and we drop all the indices. Also, I think I might have messed up some indices, not sure, however I currently arrive at
(λ/2)*Ʃmkl ∂2um/∂xk∂xl=m ∂2tui, i=1,2 (or x,y, whatever)
Now I can look...