  Inspired by the recent hints of lepton flavor universality violation in $b\to
s\ell\ell$ and $b\to c\ell\nu$ transitions, we study lepton flavor violating
exclusive $\Lambda_b\to\Lambda\ell_1^+\ell_2^-$ ($\ell_1\neq \ell_2$) decay,
which is forbidden in the Standard Model. Starting from a general effective
Hamiltonian for a $b\to s\ell_1^+\ell_2^-$ transition that includes vector and
axial-vector operators, and scalar and pseudo-scalar operators, we derive a
two-fold decay distribution of $\Lambda_b\to\Lambda\ell_1^+\ell_2^-$. The
distribution helps us to construct the differential branching ratio and the
lepton side forward-backward asymmetry, which are studied in a vector
leptoquark model. The parameter space of the vector leptoquark model is
constrained by low energy observables.
