The origin of the words "lyre of Orpheus" can be traced back to a figure in Greek mythology. Orpheus was a talented minstrel who could charm even inanimate objects with his music. His instrument of choice was the lyre and he used it with great skill and talent to attempt to charm the ruler of the Underworld into giving back Orpheus's dead wife.
However the Lyre of Orpheus also refers to a novel by Robertson Davies. His novel was the last in a trilogy and so the Lyre of Orpheus's purpose was to finish out the trilogy. Further the novel is about the tribulations of someone who sets about finishing writing an unfinished opera as part of a PhD program. There is an underlying theme in the subplots of this complicated story that mirrors its mythological origins: "the lyre of Orpheus opens the door to the underworld of feeling.”
The purpose of the lyre of Orpheus then depends on your viewpoint of either the original mythology or the novel.