I believe in one quest an NPC (during the main scenario quests for Gridania...the NPC at the top of the lethe who is afraid of heights. I think his name is Theodore.) tells you the history of the lethe. It is believed by the devout that, during the Calamity, the earth was shattered in the Shroud in that section. It would have been impossible for people to traverse that section of the Shroud any longer, but Nophica (the Matron whom it is named for) stepped in and allowed that passageway to exist via nature.

I personally have very little to go on as to how the name came to be. I'm thinking some form of irony...but that's all I can think up.