  The rare baryonic decay $\Lambda_b\to \Lambda(\to p\pi^-)\mu^+\mu^-$ provides
valuable complementary information compared to the corresponding mesonic $b\to
s\mu^+\mu^-$ transition. In this paper, using the latest high-precision lattice
QCD calculation of the $\Lambda_b\to\Lambda$ transition form factors, we study
this interesting decay within the aligned two-Higgs-doublet model, paying
particularly attention to effects of the chirality-flipped operators generated
by the charged scalars. In order to extract the full set of angular
coefficients in this decay, we consider the following ten angular observables
that can be derived from the analysis of the subsequent parity-violating
$\Lambda\to p\pi^-$ decay: the differential branching fraction ${\rm d}{\cal
B}/{\rm d}q^2$, the longitudinal polarization fraction $F_L$, the lepton-,
hadron- and combined lepton-hadron-side forward-backward asymmetries $A_{\rm
FB}^\ell$, $A_{\rm FB}^\Lambda$ and $A_{\rm FB}^{\ell\Lambda}$, as well as the
other five asymmetry observables $Y_i$~($i={\rm 2,\,3s,\,3sc,\,4s,\,4sc}$).
Detailed numerical comparisons are made between the SM and NP values for these
angular observables. It is found that, under the constraints from the inclusive
$B\to X_s\gamma$ branching fraction and the latest global fit results of $b\to
s\ell\ell$ data, the contributions of right-handed semileptonic operators
$O^{\prime}_{9,10}$, besides reconciling the $P_5^{\prime}$ anomaly observed in
$B^0\to K^{\ast 0}\mu^+\mu^-$ decay, could also enhance the values of ${\rm
d}{\cal B}/{\rm d}q^2$ and $A_{\rm FB}^\ell$ in the bin $[15,20]~{\rm GeV}^2$,
leading to results consistent with the current LHCb measurements.
