A word for “lip” appearing only in its plural form pempi in 1964 notes on the parts of the mouth, where it was related to Q. pé “the closed mouth” (PE17/126). In 1968 notes on monosyllabic nouns, Tolkien said the primitive ✶pē “lip” was reduplicated to ✶pē̆pe; this is likely connected to an irregular plural form péti in the (untranslated) phrase et i péti “✱out of the mouth/lips”, with dissimilation of the second p to t as suggested by Patrick Wynne (VT47/35): ✱pēpi > péti. The 1964 form pempe is probably also the result of reduplication, likely ✱peñ-peñ > pempe(ñ), since √PEÑ was the usual root for “lip” (PE21/70; PE19/102).
Conceptual Development: The earliest “lip” word was ᴱQ. kilme from the Qenya Lexicon of the 1910s under the early root ᴱ√KILI “edge” (QL/46), a form also appearing in the contemporaneous Poetic and Mythological Words of Eldarissa (PME/46). A similar form ᴱQ. kilma “lip” appeared in a list of body parts from the 1920s, along with an alternate word ᴱQ. kaile “lip” (PE14/117). There are no signs of these early lip-words after that point.
Neo-Quenya: Tolkien also sometimes used Q. pé for “lip”; see that entry for discussion. For purposes of Neo-Quenya, I recommend using Q. pé mainly for “closed mouth” and pempë for a single “lip”. However, the dual form peu of pé was used of “the two lips, the mouth-opening” (VT39/9), which I would use for “a pair of lips for one person (open or closed)”, functioning as an irregular dual of pempë.
This root has a long history in Tolkien’s development of the Elvish languages, but its exact meaning is hard to determine because Tolkien rarely translated the root itself. The earliest appearance of the root was as unglossed ᴱ√LIPI from the Qenya Lexicon of the 1910s where Tolkien indicated it might be a dialectical variant of ᴱ√LIQI “flow, water; clear, transparent”; it had derivatives like ᴱQ. lipte- “to drip”, ᴱQ. litl “a tiny drop”, and ᴱQ. limpe “elfwine” (QL/54). It also had derivatives in the contemporaneous Gnomish Lexicon such as G. lib “drop, gout”, G. lib- “to drip”, G. limp(elis) “the drink of the fairies” (GL/54). I think the most likely meaning of this early root was “✱drip, drop”.
In The Etymologies of the 1930s, the root for “drip” was ᴹ√LIB. ᴹ√LIP appeared, but it was unglossed and its only derivative was ᴹQ. limpe “wine” (Ety/LIB¹, LIP). Thus it seems Tolkien split up the root from the 1910s, though exactly how isn’t clear. The last known mention of this root is as √LIP “oil” (without any derivatives) in a currently unpublished set of notes from 1968 (VT44/15). Wynne, Smith, and Hostetter suggested this might be connect to a (rejected) name for Christ: Q. Elpino, perhaps meaning “✱anointed” (VT44/15). It is unclear whether this √LIP “oil” was connect to its earlier iterations from which limpe “wine” was derived, or if it is was a reemergence of a different root such as ᴱ√ILI “shine oily” as suggested by Wynne, Smith, and Hostetter (VT44/20 note #7).