  LiB, a predicted layered compound analogous to the MgB$_2$ superconductor,
has been recently synthesized via cold compression and quenched to ambient
pressure, yet its superconducting properties have not been measured. According
to prior isotropic superconductivity calculations, the critical temperature
($T_{\rm{c}}$) was expected to be only 10$-$15 K. Using the anisotropic
Migdal-Eliashberg formalism, we show that the $T_{\rm{c}}$ may actually exceed
32 K. Our analysis of the contribution from different electronic states helps
explain the detrimental effect of pressure and doping on the compound's
superconducting properties. In the search for related superconductors, we
screened Li-Mg-B binary and ternary layered materials and found metastable
phases with $T_{\rm{c}}$ close to or even 10$-$20% above the record 39 K value
in MgB$_2$. Our reexamination of the Li-B binary phase stability reveals a
possible route to synthesize the LiB superconductor at lower pressures readily
achievable in multianvil cells.
