  Based on $6.1~\mathrm{fb}^{-1}$ of $e^+e^-$ annihilation data collected at
center-of-mass energies from 4.600~GeV to 4.843~GeV with the BESIII detector at
the BEPCII collider, a partial wave analysis of
$\Lambda_c^+\to\Lambda\pi^+\eta$ is performed, and branching fractions and
decay asymmetry parameters of intermediate processes are determined. The
process $\Lambda_c^+\to\Lambda a_0(980)^+$ is observed for the first time, and
evidence for the pentaquark candidate $\Sigma(1380)^+$ decaying into
$\Lambda\pi^+$ is found with statistical significance larger than $3\sigma$.
The branching fraction product $\mathcal{B}(\Lambda_{c}^{+} \to \Lambda
a_0(980)^+) \; \mathcal{B}( a_0(980)^+ \to \pi^{+}\eta)$ is determined to be
$(1.05 \pm 0.16_{\mathrm{stat}} \pm 0.05_{\mathrm{syst}} \pm
0.07_{\mathrm{ext}})\%$, which is larger than theoretical calculations by $1 -
2$ orders of magnitude. Here the third (external) systematic is from
$\mathcal{B}(\Lambda_{c}^{+} \to \Lambda \pi^+ \eta)$. Finally, we precisely
obtain the absolute branching fraction $\mathcal{B}(\Lambda_{c}^{+} \to \Lambda
\pi^+ \eta) = (1.94 \pm 0.07_{\mathrm{stat}} \pm 0.11_{\mathrm{syst}})\%$.
