From my brief research, I'd say that the 'muller' part is indeed from 'müller' meaning "a miller" …one who grinds or mills grains.
The more interesting part is the first syllable that I've seen in a number of German names but was unsure of the origin. (Now I encourage others if I am wrong). But it seems to me that the first syllable comes from 'liege' which I believe is ultimately related to the word "allegiance" ... or some word similar to it ... please see: http://en.wikipedia.org/wiki/Liege
So, I'd offer that your friend's name likely means something like “the miller who had allegiances to the king …or duke … or earl, etc. Basically, the family name came about in the Middle Ages when the family was a miller for whatever aristocracy was above their class.