Based on 6.1 fb^{-1} of e^{+}e^{-} annihilation data collected at center-of-mass energies from 4.600 to 4.843 GeV with the BESIII detector at the BEPCII collider, a partial wave analysis of Λ_{c}^{+}→Λπ^{+}η is performed, and branching fractions and decay asymmetry parameters of intermediate processes are determined. The process Λ_{c}^{+}→Λa_{0}(980)^{+} is observed for the first time, and evidence for the pentaquark candidate Σ(1380)^{+} decaying into Λπ^{+} is found with statistical significance larger than 3σ with mass and width fixed to theoretical predictions. The branching fraction product B[Λ_{c}^{+}→Λa_{0}(980)^{+}]B[a_{0}(980)^{+}→π^{+}η] is determined to be (1.05±0.16_{stat}±0.05_{syst}±0.07_{ext})%, which is larger than theoretical calculations by 1-2 orders of magnitude. Here the third (external) systematic is from B(Λ_{c}^{+}→Λπ^{+}η). Finally, we precisely obtain the absolute branching fraction B(Λ_{c}^{+}→Λπ^{+}η)=(1.94±0.07_{stat}±0.11_{syst})%.