  The lattice dynamical properties of Li$_x$BC are calculated for several
values of $x$ using density functional perturbation theory. We find that the
electron-phonon coupling parameter $\lambda$ increases monotonically with
decreasing $x$ to a maximum value of 1.4 for $x=0.125$ owing to the increasing
radius of multiply-nested Fermi surface cylinders. The B-C bond-stretching
phonon modes have frequencies which are 28% higher than the equivalent modes in
MgB$_2$. This combination results in a $T_c$ of about 65 K for $x=0.5$.
