Using the Bethe-Salpeter equation (BSE) we investigate the forward-backward asymmetries $( A _{FB}) $ in $\Lambda_b \rightarrow \Lambda l^+ l^-(l=e,\mu,\tau)$ in the quark-diquark model. This approach provides precise form factors that are different from those of QCD sum rules. We calculate the rare decay form factors for $\Lambda_b \rightarrow \Lambda l^+ l^-$ and investigate the (integrated) forward-backward asymmetries in these decay channels. We find that the integrated $A^l_{FB}$, $\bar{A}^l_{FB}(\Lambda_b \rightarrow \Lambda e^+ e^-) \simeq -0.1371 $, $\bar{A}^l_{FB}(\Lambda_b \rightarrow \Lambda \mu^+ \mu^- ) \simeq -0.1376 $, $\bar{A}^l_{FB}(\Lambda_b \rightarrow \Lambda \tau^+ \tau^-) \simeq -0.1053 $, the hadron side asymmetries $\bar{A}^h_{FB}(\Lambda_b \rightarrow \Lambda \mu^+ \mu^-)\simeq -0.2315$, the lepton-hadron side asymmetries $\bar{A}^{lh}_{FB}(\Lambda_b \rightarrow \Lambda \mu^+ \mu^-)\simeq 0.0827$, the longitudinal polarization fractions $\bar{F}_L(\Lambda_b \rightarrow \Lambda \mu^+ \mu^-)\simeq 0.5681$. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.