  In this work, we make a theoretical study on the $p \bar p \rightarrow
\Lambda \bar\Lambda \eta$ reaction for antiproton beam energy from threshold to
4GeV within an effective Lagrangian approach and isobar model. By assuming this
reaction is dominated by the excitation of $\Lambda$ and $\bar \Lambda$
resonances in intermediate states, we calculate the total cross sections and
give the predictions of the angular distribution and invariant mass spectrum of
final particles. In particular, we discuss the possibility to verify the
existence of a narrow $\Lambda$ resonance found in the process of $K^- p\to
\eta \Lambda$ in the present reaction. It shows that the $p \bar p \rightarrow
\bar \Lambda \Lambda \eta$ reaction can provide us with valuable information
about the $\Lambda$ resonances having significant couplings to $\bar K N$ and
$\Lambda\eta$ channels. Thus the experimental data of this reaction will be a
good supplement to the $\bar K N\to\eta \Lambda$ scattering data for studying
$\Lambda$ resonances.
