  We study the steady-state motion of mode III cracks propagating on a lattice
exhibiting viscoelastic dynamics. The introduction of a Kelvin viscosity $\eta$
allows for a direct comparison between lattice results and continuum
treatments. Utilizing both numerical and analytical (Wiener-Hopf) techniques,
we explore this comparison as a function of the driving displacement $\Delta$
and the number of transverse sites $N$. At any $N$, the continuum theory misses
the lattice-trapping phenomenon; this is well-known, but the introduction of
$\eta$ introduces some new twists. More importantly, for large $N$ even at
large $\Delta$, the standard two-dimensional elastodynamics approach completely
misses the $\eta$-dependent velocity selection, as this selection disappears
completely in the leading order naive continuum limit of the lattice problem.
