The electrostatic heavy-ion storage ring, ELISA is utilized to measure the lifetime of the metastable $1s2s2p{}^{4}{P}_{5/2}$ level of the ${\mathrm{He}}^{\ensuremath{-}}$ ion together with the average lifetime of the ${}^{4}{P}_{1/2}$ and ${}^{4}{P}_{3/2}$ levels. This storage ring allows lifetime measurements to be performed without the influence of magnetic fields, and at temperatures below $\ensuremath{-}50\ifmmode^\circ\else\textdegree\fi{}\mathrm{C},$ which reduces the photodetachment of ${\mathrm{He}}^{\ensuremath{-}}$ due to blackbody radiation. The lifetime of the ${}^{4}{P}_{5/2}$ level is determined to be $365\ifmmode\pm\else\textpm\fi{}3 \ensuremath{\mu}\mathrm{s},$ in agreement with, but more accurate than, a previous magnetic storage ring measurement, and 6% longer than the lifetime recently reported utilizing an electrostatic ion trap [Wolf et al., Phys. Rev. A 59, 267 (1999)]. The average lifetime of the ${}^{4}{P}_{1/2}$ and ${}^{4}{P}_{3/2}$ levels is determined to be $11.1\ifmmode\pm\else\textpm\fi{}0.3 \ensuremath{\mu}\mathrm{s},$ in agreement with theoretical predictions, but about 25% longer than the reported value from the electrostatic ion trap experiment.