William Shakespeare was a great biographer who wrote plays based on many contemporary facts. Shakespeare's talents are well known and respected. Several of his plays however were incomplete, including a play about The League.
According to the rules of the LOEG-universe this can't be the real Shakepeare from our world but has to be a character out of a piece of fiction. Because of hints given by Moore in "The Black Dossier" it seems to be clear that this can only be the Shakespeare who appears in Neil Gaiman's famous "Sandman"-series. In this series Shakespeare and Dream have a deal: Shakespeare gets the gift to write the best plays ever written and in return he has to write two plays for Dream aka Lord Lord Morpheus (i.e. "A Midsummer Night's Dream" and "The Tempest"). In reality as well as in the Sandman-universe, "The Tempest" is Shakespeare's last play, but Moore alters here the given facts once more, because in the LOEG-universe there is another faerie-related play by Shakespeare, "Faerie's Fortunes Founded", which is kind of a prequel to "The Tempest". Having only written two scenes of this last play, Shakespeare dies - and his last sentence is as well Queen Gloriana's sigh as his own: "And would I know Dream's moonlit towns again."
The editor of the facsimile of this scenes doesn't know for sure if Shakespeare wrote "Faerie's Fortunes Founded" indeed for the faerie-hating King Jacob I, but we know better: He wrote it on behalf of Lord Morpheus or at least on behalf of another faerie-friend from the realm of twilight.