  We compute the two-loop term in the perturbation series for the quark-mass in
the lattice Heavy Quark Effective Theory. This is an ingredient in the matching
factor required to obtain the $b$-quark mass from lattice simulations of the
HQET. Combining our calculations with numerical results from the APE
collaboration, we find, at two-loop order, $\bar m_b \equiv
m_b^{\bar{MS}}(m_b^{\bar{MS}}) =4.41\pm 0.05\pm 0.10 $GeV. It was expected that
the two-loop term would have a significant effect and this is indeed what we
find. Depending on the choice of "reasonable" coupling constant in the one-loop
estimates the result for $\bar m_b$ can change by several hundred MeV when the
two-loop terms are included.
