Questions first, then my rough estimations:
1) Is it possible to perform moon laser ranging with amateur motorized 114mm telescope? My calculations suggest that for 1mJ laser it should receive ~2 photons per source 1mJ laser pulse.
2) Given that we already talking about individual photons, how it was possible to perform moon laser ranging BEFORE retro-reflectors were deployed to the moon? Retroreflector sends back light in ~1arcsecond angle, while bare lunar sufrace - in ~6 archours, which means we supposed to receive signal ~(6*60*60)^2 = 4.5*10^8 weaker, i.e. even with 2.5 meter telescopes we are talking 1 photon per 250 1J pulses.
My rough estimations: Given that atmosphere turbulence limits telescope resolution to ~1 arcsecond (adaptive optics was not available when laser ranging experiments started, nor it is available now for amateurs), if we use telescope with diameter larger than ~150mm (so that we are limited by atmosphere, not diffraction) to expand the laser beam we will get ~1939x1939 meter illuminated area on the moon surface (tan(1arcsec)*400'000km). Which means only 1/(1939*1939) part of our energy will reach reflector.
Retroreflector is ~1x1 meter in size. It will reflect the light with same beam divergence - 1arcsecond. Too sad, as diffraction limit for retro-reflector of such size is ~0.2 arcsecond.
So, if our receiving telescope has area of ~1 meter^2, we will receive again 1/(1939*1939) part of what reached the moon, so total attenuation is ~ 1.4*10^13.
If we use 532nm pulse laser with 1mJ pulse energy, it will emit 2.67*10^15 photons, which means we are going to receive ~190 photons per pulse. Sounds realistic.
These calculations suggests that 114mm amateur telescope should be able to detect 2 photon per pulse - again should be detectable statistically.