Not practiced very much any more, but a medical dictionary from the turn of the 20th century notes that it "has been" used in the treatment of aneurysm, by which I think it means a stroke. The Greek root here is limós, hunger, which also appears as the second half of bulimia (where the first is an intensifying prefix derived from bous, ox -- go fig). Possibly this could be extended to modern detoxifying therapies, but my understanding is those involve more than simple fasting but include purgative doses. On the other hand, I can definitely see considering going cold turkey as a sort of limited limotherapy.
It's not limotherapy -- it's Yom Kippur.