Strong red low-temperature photoluminescence results from Li diffusion of as-grown GaP crystals prepared from the vapor by the wet ${\mathrm{H}}_{2}$ method, or from Ga solution with O doping. The luminescence spectrum contains sharp strong no-phonon lines and many well-resolved phonon replicas. Four no-phonon lines can be seen at zero field. The spacings between these lines are approximately consistent with a model in which the luminescence arises from the decay of an exciton bound by \ensuremath{\sim} 0.24 eV to an axial (${C}_{3v}$) center. The $J\ensuremath{-}J$ and crystal-field splittings are 1.1 and 3.4 meV. The symmetry axis is shown to be $〈111〉$ from detailed magneto-optical studies of the no-phonon lines, and the electron and hole $g$ values are determined from an analysis for strong crystal field, ${g}_{e}=1.76\ifmmode\pm\else\textpm\fi{}0.14$, ${g}_{h}=1.04\ifmmode\pm\else\textpm\fi{}0.05$. Use of this form of analysis is suggested by the degree of mixing of the $J\ensuremath{-}J$-split states by the crystal field, indicated by the relative oscillator strengths of the no-phonon lines. The chemical identity of components of this axial center has been determined from isotope experiments. The substitution ${\mathrm{O}}^{16}$\ensuremath{\rightarrow}${\mathrm{O}}^{18}$ increases the no-phonon line energies by 0.8 meV, and shifts some of the many local-mode lines resolved in the phonon wing of the luminescence spectrum. Only changes in local-mode energies occur for the substitution ${\mathrm{Li}}^{7}$\ensuremath{\rightarrow}${\mathrm{Li}}^{6}$, but these changes are generally larger than for O. The form of the true local-mode replicas for crystals containing roughly equal amounts of ${\mathrm{Li}}^{6}$ and ${\mathrm{Li}}^{7}$ proves that the center contains at least two inequivalent Li atoms. The simplest model for the center consistent with all the detailed experimental evidence is ${\mathrm{Li}}_{I}\ensuremath{-}{\mathrm{Li}}_{\mathrm{Ga}}\ensuremath{-}{\mathrm{O}}_{\mathrm{P}}$ ($I$=interstitial). This complex is isoelectronic with the Ga-P atom pair it replaces, can produce efficient low-temperature bound-exciton luminescence with decay time consistent with experiment (\ensuremath{\sim} 200 nsec for decay allowed by electric dipole selection rules), and has no free spin in the final state. The temperature quenching rate of the Li-Li-O luminescence is large compared with the familiar red Zn-O luminescence because of the high degree of compensation produced by Li diffusion, and the Li-Li-O photo- and electroluminescence efficiencies are negligible near 300 \ifmmode^\circ\else\textdegree\fi{}K. The associate ${V}_{\mathrm{Ga}}\ensuremath{-}{\mathrm{O}}_{\mathrm{P}}$ ($V$=vacancy) is necessary for the formation of the Li-Li-O centers. Evidence is presented that a significant proportion of the substitutional O exists in these associates before Li diffusion for GaP crystals grown or annealed below 1100 \ifmmode^\circ\else\textdegree\fi{}C. Apparently, the ${V}_{\mathrm{Ga}}\ensuremath{-}{\mathrm{O}}_{\mathrm{P}}$ associate is not stable significantly above 1100 \ifmmode^\circ\else\textdegree\fi{}C, while association is essentially quenched at $T\ensuremath{\lesssim}700$ \ifmmode^\circ\else\textdegree\fi{}C. The behavior of ${V}_{\mathrm{Ga}}$ in GaP can be studied very conveniently from the optical properties of the Li-Li-O associate. In addition, the efficiency of O-doping techniques for GaP crystals grown by different methods can be assessed easily and with high accuracy and sensitivity by purely optical measurements, using appropriate annealing techniques together with ${\mathrm{O}}^{18}$ doping.