We consider extensions of the Standard Model by vectorlike leptons and set limits on a new charged lepton, $e_4^±$, using the ATLAS search for anomalous production of multi-lepton events. It is assumed that only one Standard Model lepton, namely the muon, dominantly mixes with vectorlike leptons resulting in possible decays $e_4^± \to W^± ν_μ$, $e_4^± \to Zμ^±$, and $e_4^± \to h μ^±$. We derive generally applicable limits on the new lepton treating the branching ratios for these processes as free variables. We further interpret the general limits in two scenarios with $e_4^±$ originating predominantly from either the $SU(2)$ doublet or the $SU(2)$ singlet. The doublet case is more constrained as a result of larger production cross-section and extra production processes $e_4^± ν_4$ and $ν_4ν_4$ in addition to $e_4^+ e_4^-$, where $ν_4$ is a new neutral state accompanying $e_4$. We find that some combinations of branching ratios are poorly constrained, whereas some are constrained up to masses of more than 500 GeV. In the doublet case, assuming BR$(ν_4→ Wμ) = 1$, all masses below about 300 GeV are ruled out. Even if this condition is relaxed and additional decay modes, $ν_4 \to Z ν_μ$ and $ν_4 \to h ν_μ$, are allowed, below the Higgs threshold still almost all of the parameter space (of independent branching ratios) is ruled out. Nevertheless, even assuming the maximal production cross-section, which coincides with the doublet case, the new charged lepton can still be as light as the LEP-II limit allows. We discuss several possible improvements of current experimental analyses that would dramatically reduce the allowed parameter space, even with current data. ; Comment: 24 pages, 11 figures