  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 $\bar{F}_L(\Lambda_b \rightarrow \Lambda \mu^+ \mu^-)\simeq 0.5681$.
