Board Thread:General Discussion/@comment-24283746-20140116090009/@comment-53539-20150616170131

^This may be true per translation purposes, but not true per origin of their names. Their names are based on "L and R" (left and right) and are portmanteau of that and the names of two characters from Fist of the North Star ken and Rin.

Their names are basically meant to be read something like "Mirror sound left" and "mirror sound right" and reference to "reflect sound" or echoing. Miku is a reference to the moment a person speaks and Luka is a reference to sound that has traveled a while.