We have performed inelastic neutron scattering measurements on a powder sample of the superconductor lithium iron selenide hydroxide Li$_{1-x}$Fe$_{x}$ODFe$_{1-y}$Se ($x simeq 0.16, y simeq 0.02$, $T_{rm c} = 41$,K). The spectrum shows an enhanced intensity below $T_{rm c}$ over an energy range $0.64times2Delta < E < 2Delta$, where $Delta$ is the superconducting gap, with maxima at the wave vectors $Q_1 simeq 1.46$,AA$^{-1}$ and $Q_2 simeq 1.97$,AA$^{-1}$. The behavior of this feature is consistent with the spin resonance mode found in other unconventional superconductors, and strongly resembles the spin resonance observed in the spectrum of the molecular-intercalated iron selenide, Li$_{0.6}$(ND$_{2}$)$_{0.2}$(ND$_{3}$)$_{0.8}$Fe$_{2}$Se$_{2}$. The signal can be described with a characteristic two-dimensional wave vector $(pi, 0.67pi)$ in the Brillouin zone of the iron square lattice, consistent with the nesting vector between electron Fermi sheets.