The root ᴱ√TYETE appeared in the Qenya Lexicon of the 1910s with the gloss “give suck” and derivatives ᴱQ. tyetl “babe, a tiny baby” and ᴱQ. tyetse “teat” (QL/50). I think it is worth positing a Neo-Root ᴺ√TYET to salvage some of these early words.
Quenya
tye
pronoun. you (familiar), thee
tyet-
verb. to suckle, nurse
A neologism for “to suckle, nurse” coined by Helge Fauskanger for his NQNT (NQNT), based on the early root ᴱ√TYETE “give suck”.