Are there any Germanic cognates to "lithe"?

          When winter first begins to bite
               and stones crack in the frosty night,
          when pools are black and trees are bare,
               ’tis evil in the Wild to fare.

In this time of the sun’s greatest ebb when our hearts are gladdened knowing that with Midwinter come and gone, winter is now half over, my thoughts are drawn to Midwinter yule’s warmer twin, Midsummer’s lithe.

In Tolkien’s writings, lithe was the name for the days around Midsummer’s Day when the nights are shortest, just as yule was (and still is) the name for the days around Midwinter’s Day when the days are shortest.

Lithe is today’s spelling of Old English līþa. But outside the Shire, lithe is now a word almost unknown to most of us. It seems to have no children in today’s English, nor did I find any words kin to it in our sister-tongues. The Wiktionary link I have given above tells no more than this little-trusted tale (bold mine):

Apparently related to liþe (“mild”)’ probably cognate with Serbo-Croatian ljeto, Czech léto, Polish lato, Russian лето (léto, “summer, year”).

How could an Old English word about summer come to us without kindred words in any tongue nearer our own than in the far-off speech of our cousins’ cousins’ cousins?

Are there any that are nearer to us than those?

Solution 1:

The term lithe does have a Germanic cognate as explained in Etymonline

Old English liðe "soft, mild, gentle, calm, meek," also, of persons, "gracious, kind, agreeable," *from Proto-Germanic *linthja - (source also of Old Saxon lithi "soft, mild, gentle," Old High German lindi, German lind, Old Norse linr "soft to the touch, gentle, mild, agreeable," with characteristic loss of "n" before "th" in English), from PIE root *lento- "flexible" (source also of Latin lentus "flexible, pliant, slow," Sanskrit lithi).

The loss of a nasal sound appears to be a characteristic of Old English after a vowel and before a consonant as shown in:

Old English and Its Closest Relatives: A Survey of the Earliest Germanic Languages by Orrin W. Robinson:

In Old English we would than have, in addition to the shift of *þ to ð, a common type of change involving the loss of a nasal after a vowel and before a consonant, with a lengthening of the vowel to compensate for the loss of the nasal.

See also the Wikipedia article on the Ingvaeonic nasal spirant law, which further describes this phenomenon by which nasals were lost before fricatives in a certain branch of the Germanic languages.