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.
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