In this work, we investigate the charmless non-leptonic two-body ${\Lambda }_b$ decays within the framework of final-state rescattering mechanism. Using this framework, we evaluate the relevant hadronic triangle diagrams by performing the loop integrations, retaining both their absorptive and dispersive parts. Based on the established formalism, we analyze the ${\Lambda }_b\to N^{*}(1535,1520)M$ decay processes with $M=K_S,K_0^{*}(700)$, $f_0(500,980),\rho (770),{\bar{K}}^{*0}$, $\varphi$, and predict various physical observables, such as their branching ratios, direct and partial-wave $CP$ asymmetries, as well as decay asymmetry parameters. These two-body decay processes are expected to contribute primarily to the subsequent four-body decay channels, such as ${\Lambda }_b^0\to p{\pi }^{-}{\pi }^{+}{\pi }^{-}$, whose $CP$ asymmetry measurements will be accessible at the LHCb experiment.