We have evaluated the application of a lutetium yttrium oxyorthosilicate (LYSO) based detector to single-shot positron annihilation lifetime spectroscopy. We compare this detector directly with a similarly configured PbWO 4 scintillator, which is the usual choice for such measurements. We find that the signal to noise ratio obtained using LYSO is around three times higher than that obtained using PbWO 4 for measurements of Ps excited to longer-lived (Rydberg) levels, or when they are ionized soon after production. This is due to the much higher light output for LYSO (75% and 1% of NaI for LYSO and PbWO 4 respectively). We conclude that LYSO is an ideal scintillator for single-shot measurements of positronium production and excitation performed using a low-intensity pulsed positron beam.