LLR & Orbital Motion
Well it kind of makes sense, but what is important here is the Earth's velocity relative to the Moon, not the Sun!

Roughly: the Moon-Earth separation is 400,000 km and a complete orbit takes 27 days. Thus the relative orbital speed is more like 1 km/s and so a 20km diameter beam easily covers the expected relative motion of about 2.5 km during the 2.5s round trip.