  The reaction $K^-p\rightarrow\Lambda\eta$ at low energies is studied with a
chiral quark model approach. Good descriptions of the existing experimental
data are obtained. It is found that $\Lambda(1670)$ dominates the reaction
around threshold. Furthermore, $u$- and $t$-channel backgrounds play crucial
roles in this reaction as well. The contributions from the $D$-wave state
$\Lambda(1690)$ are negligibly small for its tiny coupling to $\eta\Lambda$. To
understand the strong coupling properties of the low-lying negative parity
$\Lambda$ resonances extracted from the $\bar{K}N$ scattering, we further study
their strong decays. It is found that these resonances are most likely mixed
states between different configurations. Considering these low-lying negative
parity $\Lambda$ resonances as mixed three-quark states, we can reasonably
understand both their strong decay properties from Particle Data Group and
their strong coupling properties extracted from the $\bar{K}N$ scattering. As a
byproduct, we also predict the strong decay properties of the missing $D$-wave
state $|\Lambda\frac{3}{2}^-\ >_3$ with a mass of $\sim1.8$ GeV. We suggest our
experimental colleagues search it in the $\Sigma(1385)\pi$ and $\Sigma\pi$
channels.
