"...he followed his directions to the menís room on the lower level..."
Does "lower level" just vaguely suggests "downstairs" without specifying which level it is? Or precisely refers to the underground basement part of a building?
"The lower level" just means the (the only one) level lower than the one he is on; not neccessarily basement. Because "the" is used, there isn't a choice of lower levels. Either there is only one lower level, or the author is refering us to a lower level he expects us to know about. If it was "a" lower level, then it would mean any level lower than the one he is on.