  We calculate the weak transition form factors of the
$\Lambda_b\to\Lambda(1520)$ transition, and further calculate the angular
distributions of the rare decays $\Lambda_b\to\Lambda(1520)(\to
N\bar{K})\ell^{+}\ell^{-}$ ($N\bar{K}=\{pK^-,n\bar{K}^0\}$) with unpolarized
$\Lambda_b$ and massive leptons. The form factors are calculated by the
three-body light-front quark model with the support of numerical wave functions
of $\Lambda_b$ and $\Lambda(1520)$ from solving the semirelativistic potential
model associated with the Gaussian expansion method. By fitting the mass
spectrum of the observed single bottom and charmed baryons, the parameters of
the potential model are fixed, so this strategy can avoid the uncertainties
arising from the choice of a simple harmonic oscillator wave function of the
baryons. With more data accumulated in the LHCb experiment, our result can help
for exploring the $\Lambda_b\to\Lambda(1520)\ell^+\ell^-$ decay and deepen our
understanding on the $b\to s\ell^+\ell^-$ processes.
