In 2015, the LHCb collaboration has measured the differential branching ratio dB dq 2 , the lepton-and hadron-side forward-backward asymmetries, denoted by A F B and A Λ F B , respectively in the range 15 < q 2 (= s) < 20 GeV 2 with 3 fb −1 of data. Motivated by these measurements, we perform an analysis of q 2 dependent Λ b → Λ(→ pπ)µ + µ − angular observables at large-and low-recoil in the SM and in a family non-universal Z model. The exclusive Λ b → Λ transition is governed by the form factors and in the present study we use the recently performed high-precision lattice QCD calculations that have well controlled uncertainties especially in 15 < s < 20 GeV 2 bin. Using the full fourfolded angular distribution of Λ b → Λ(→ pπ)µ + µ − decay, first of all we focus on the calculations of experimentally measured dB ds , A F B and A Λ F B in the SM and compare their numerical values with the measurements in appropriate bins of s. In case of the possible discrepancy between the SM prediction and measurements, we try to see if these can be accommodated though the extra neutral Z boson. We find that in the dimuon momentum range 15 < s < 20 GeV 2 the value of dB ds and central value of A F B in Z model is compatible with the measured values. In addition, the fraction of longitudinal polarization of the dimuon F L is measured to be 0.61 +0.11 −0.14 ± 0.03 in 15 < s < 20 GeV 2 at the LHCb. We find that in this bin the value found in the Z model is close to the observed values. After comparing the results of these observables, we have proposed the other observables such as α i and α ( ) i with i = θ , θ Λ , φ, L, U and coefficients of different foldings P 1,••• ,9 in different bins of s in the SM and Z model. We illustrate that the experimental observations of the s-dependent angular observables calculated here in several bins of s can help to test the predictions of the SM and unravel NP contributions arises due to Z model in the Λ b → Λ(→ pπ)µ + µ − decays.