Valence and excited dipole-bound states of the ${\mathrm{LiH}}^{\mathrm{\ensuremath{-}}}$ anion are calculated with the recently developed electron-attachment equation-of-motion coupled-cluster technique. It is found that the first dipole-bound state of ${\mathrm{LiH}}^{\mathrm{\ensuremath{-}}}$ corresponds to the second dissociation channel ${\mathrm{LiH}}^{\mathrm{\ensuremath{-}}}{\ensuremath{\rightarrow}\mathrm{Li}}^{\mathrm{\ensuremath{-}}}{(}^{1}S)+\mathrm{H}{(}^{2}S).$ The second (excited) dipole-bound state of ${\mathrm{LiH}}^{\mathrm{\ensuremath{-}}}$ is below the neutral ground-state potential energy curve only for some range of the Li-H internuclear distance. This state appears at bond lengths larger than $\ensuremath{\approx}2.0\AA{}$ and decays at Li-H distances longer than \ensuremath{\approx}4.2 \AA{}, where the dipole moment of LiH becomes smaller than the critical value of 2.5 D. The adiabatic electron affinity of LiH calculated at the coupled-cluster level with the iterative inclusion of all single, double, and triple excitations and a large atomic natural orbital basis set is 0.327 eV, almost matching the recently obtained experimental value of $0.342\ifmmode\pm\else\textpm\fi{}0.012\mathrm{eV}.$