The rare baryonic decay Lambda _brightarrow Lambda (rightarrow ppi ^-)mu ^+mu ^- provides valuable complementary information compared to the corresponding mesonic brightarrow smu ^+mu ^- transition. In this paper, using the latest high-precision lattice QCD calculation of the Lambda _brightarrow Lambda transition form factors, we study this interesting decay within the aligned two-Higgs-doublet model, paying particularly attention to the 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, which can be derived from the analysis of the subsequent parity-violating Lambda rightarrow ppi ^- decay: the differential branching fraction mathrm{d}mathcal{B}/mathrm{d}q^2, the longitudinal polarization fraction F_mathrm{L}, the lepton-, hadron- and combined lepton–hadron-side forward–backward asymmetries A_mathrm{FB}^ell , A_mathrm{FB}^Lambda and A_mathrm{FB}^{ell Lambda }, as well as the other five asymmetry observables Y_i (i=mathrm{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 Brightarrow X_sgamma branching fraction and the latest global fit results of brightarrow sell ell data, the contributions of right-handed semileptonic operators O^{prime }_{9,10}, besides reconciling the P_5^{prime } anomaly observed in B^0rightarrow K^{*0}mu ^+mu ^- decay, could also enhance the values of mathrm{d}mathcal{B}/mathrm{d}q^2 and A_mathrm{FB}^ell in the bin [15,20]~mathrm{GeV}^2, leading to results consistent with the current LHCb measurements.