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 PbWO4 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 PbWO4 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 PbWO4 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.