  Based on a sample of $448.1\times10^6\ \psi(3686)$ events collected with the
BESIII detector, a study of $\psi(3686)\to\Lambda\bar{\Lambda}\pi^0$ and
$\psi(3686)\to\Lambda\bar{\Lambda}\eta$ is performed. Evidence of the
isospin-violating decay $\psi(3686)\to\Lambda\bar{\Lambda}\pi^0$ is found for
the first time with a statistical significance of $3.7\sigma$, the branching
fraction $\mathcal{B}(\psi(3686)\to\Lambda\bar{\Lambda}\pi^0)$ is measured to
be $(1.42\pm0.39\pm0.59)\times10^{-6}$, and its corresponding upper limit is
determined to be $2.47\times10^{-6}$ at 90\% confidence level. A partial wave
analysis of $\psi(3686)\to\Lambda\bar{\Lambda}\eta$ shows that the peak around
$\Lambda\eta$ invariant mass threshold favors a $\Lambda^*$ resonance with mass
and width in agreement with the $\Lambda(1670)$. The branching fraction of the
$\psi(3686)\to\Lambda\bar{\Lambda}\eta$ is measured to be
$(2.34\pm0.18\pm0.52)\times10^{-5}$. The first uncertainties are statistical
and the second are systematic.
