  Motivated by the Belle measurements of the process $\Lambda_c^+\to
\eta\pi^+\Lambda$, we investigate this process by considering the contributions
from the $\Lambda(1670)$, $a_0(980)$, and $\Sigma(1385)$. In addition, we also
consider the predicted low-lying baryon $\Sigma^*(1/2^-)$. Our results
involving the $\Sigma^*(1/2^-)$ are favored by fitting to the Belle data of the
$\eta\Lambda$ and $\pi^+\Lambda$ invariant mass distributions. Furthermore, we
predict the $\eta\pi^+$ invariant mass distribution and the angular
distribution $d\Gamma/d{\rm cos}\theta$, which are significantly different
depending on whether or not the contribution from the $\Sigma^*(1/2^-)$ is
considered. Finally, we show that, with the contribution from the
$\Sigma^*(1/2^-)$, the calculated Dalizt plot agrees with the Belle
measurements. Future precise measurements of the process $\Lambda_c^+\to
\eta\pi^+\Lambda$ could shed further light on the existence of the low-lying
$\Sigma^*(1/2^-)$.
