  We analyze the baryonic semilepton decay $\Lambda_{b} \rightarrow$ $\Lambda
\mu^{+} \mu^{-}$ in the scalar leptoquark models with $X(3,2,7/6)$ and
$X(3,2,1/6)$ states, respectively. We also discuss the effects of this two NP
models on some physical observables. For some measured observables, like the
differential decay width, the longitudinal polarization of the dilepton system,
the lepton-side forward-backward asymmetry and the baryon-side forward-backward
asymmetry, we find, the prediction values of SM are consistent with the current
data in the most $q^{2}$ ranges, where the prediction values of this two NP
models can also keep consistent with the current data with $1\sigma$. However,
in some $q^{2}$ ranges, the prediction values of SM are difficult to meet the
current data, but the contributions of this two NP models can meet them or keep
closer to them. For the double lepton polarization asymmetries, $P_{LT}$,
$P_{TL}$, $P_{NN}$ and $P_{TT}$ are sensitive to the scalar leptoquark model
$X(3,2,7/6)$ but not to $X(3,2,1/6)$. However, $P_{LN}$, $P_{NL}$, $P_{TN}$ and
$P_{NT}$ are not sensitive to this two NP models.
