The only real official in the Shire at this date was the Mayor of Michel Delving (or of the Shire), who was elected every seven years at the Free Fair on the White Downs at the Lithe, that is at Midsummer.
There are no more uses of "lithe" in the book.
Show samples from other sources
The lithe dancers seem to float across the stage.
Although Elvis is best known for his lithe, gyrating "Hound Dog" days, it is his later, weightier, gold lamé–draped self that remains the most emulated among most of his impersonators.
Alyssa Fetini -- Time Inc, 2010 -- http://www.time.com/time/specials/packages/article/0,28804,1952461_1952460_1952463,00.html#ixzz0wPA0qwrx(retrieved 08/12/10)