From the Old English month-name Liða, 'warm, gentle'
Other names
Forelithe (the Mannish months of Nárië or Nórui also corresponded closely with Lithe, without being directly related)
Note
This usage is not to be confused with that preferred by the Shire-hobbits, who used the name Lithe quite differently to refer to the days around Midsummer1
An Old English name for a summer month, Lithe was used in the Shire Calendar to refer to a period of days around Mid-year's Day. In Bree, the same name was used in a different way, and there Lithe was an entire month, the sixth of the year, roughly corresponding to modern June. It was preceded by Thrimidge, and followed by the Summerdays (the same days that the Shire-hobbits referred to by their use of the word 'Lithe').