Using 58 million and 14 million events collected by the BESII detector at the BEPC, branching fractions or upper limits for the decays and and $\Lambda \bar{\Lambda}\eta$ are measured. For the isospin violating decays, the upper limits are determined to be ${\cal B}(J/\psi \to \Lambda \bar{\Lambda}\pi^0)<6.4\times 10^{-5}{\cal B}(\psi(2S) \to \Lambda \bar{\Lambda}\pi^0)<4.9\times 10^{-5}$ at the 90% confidence level. The isospin conserving process is observed for the first time, and its branching fraction is measured to be ${\cal B}(J/\psi \to \Lambda \bar{\Lambda}\eta)=(2.62\pm 0.60\pm 0.44)\times 10^{-4}$, where the first error is statistical and the second one is systematic. No $\Lambda \bar{\Lambda}\eta\psi(2S){\cal B}(\psi(2S) \to \Lambda \bar{\Lambda}\eta)<1.2\times 10^{-4}$ is set at the 90% confidence level. Branching fractions of decays into $\Sigma^+ \pi^- bar{\Lambda}\bar{\Sigma}^- \pi^+ \Lambda$ are also reported, and the sum of these branching fractions is determined to be ${\cal B}(J/\psi \to \Sigma^+\pi^- \bar{\Lambda} + c.c.)=(1.52\pm 0.08\pm 0.16)\times 10^{-3}$.

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