  The nuclear spin-lattice relaxation time ($T_1$) of lanthanum and aluminum
nuclei in a single crystal of lanthanum aluminate doped with neodymium ions is
studied to estimate the feasibility of the dynamically polarized lanthanum
target applicable to beam experiments. The application of our interest is the
study of fundamental discrete symmetries in the spin optics of epithermal
neutrons. This study requires a highly flexible choice of the applied magnetic
field for neutron spin control and favors longer $T_1$ under lower magnetic
field and at higher temperature. The $T_1$ of $^{139}{\rm La}$ and ${}^{27}{\rm
Al}$ was measured under magnetic fields of $0.5$-$2.5$ T and at temperatures of
$0.1$-$1.5$ K and found widely distributed up to 100 h. The result suggests
that the $T_1$ can be as long as $T_1 \sim$ 1 h at $0.1$ K with a magnetic
field of $0.1$ T, which partially fulfills the requirement of the neutron beam
experiment. Possible improvements to achieve a longer $T_1$ are discussed.
