The word Q. pé was the main Quenya word for “lip(s)” for all of Tolkien’s life, but its derivation evolved over time. The root first appeared as unglossed ᴱ√PĒ in the Qenya Lexicon of the 1910s with the derivative ᴱQ. pé “the two lips, the (closed) mouth” (QL/72). The contemporaneous Gnomish Lexicon compared this Qenya word to G. beg “chin” or “beard” (GL/22), hinting that the actual root might have been ✱ᴱ√BĒ. In the Declension of Nouns from the early 1930s, the primitive form was given as PĒ “lips, mouth” (PE21/1, 38). In The Etymologies of the 1930s the root became ᴹ√PEG “(?outer) mouth” with derivative ᴹQ. pé “mouth” (Ety/PEG; EtyAC/PEG).
In Common Eldarin: Noun Structure from the early 1950s the root is given as unglossed √PEÑ (PE21/71), and in notes associated with the Quendi and Eldar essay of 1959-60 the primitive form is given as peñe (VT39/11). In both cases it was an example of a primitive form that resulted in ancient monosyllabic nouns from weak consonant loss: √PEÑ > ✶pē. In notes from the late 1960s Tolkien again gave ✶pē in a list of primitive monosyllabic nouns, but said “of these all except pe, su had probably lost a consonant in Common Eldarin”, implying the original form was actually √PĒ. But in green-note revisions made in 1970 to Outline of Phonology Tolkien had:
> ñ disappeared prehistorically, so that words such as peñ were for Quenya long monosyllabic nouns with only an initial consonant: pē (PE19/102 and note #168).
Thus it seems the lost ñ in √PEÑ was restored, though it could also be a remnant of the earlier version of this sentence from the 1950s that gave both peñ and maʒ as examples of consonant-loss.
Neo-Eldarin: For purposes of Neo-Eldarin, I think it is best to assume the root is √PEÑ.
This root first appeared in The Etymologies of the 1930s as unglossed ᴹ√PEN with extended form ᴹ√PÉNED from which the main words in its entry were derived: ᴹQ. penda “sloping down, inclined”, ᴹQ. pende “slope, downslope, declivity” and N. penn “declivity” (Ety/PEN). The last of these has a precursor in Early Noldorin Word-lists from the 1920s: ᴱN. benn “inclined, sloping” or “slanting, sloping, up or down hill”, along with a noun form ᴱN. binn “slope”, apparently derived from the adjective plural (PE13/138, 160). This earlier form is reflected on several rejected roots in The Etymologies, with ᴹ√BEND >> ᴹ√DEN >> ᴹ√PEN (EtyAC/DAT, DEN).
In later writings, Tolkien generally gave the base root as √PED, a change Tolkien seems to have introduced to avoid conflict with a new root √PEN “lack, not have” (PE17/171, 173). The root √PED was variously glossed “incline, slope” (PE17/171), “fall in steep slant, incline, slope” (PE17/173) or “slope, slant down” (WJ/375); all these notes date to 1959-60. Tolkien went to say that “strong forms [were] lost in Quenya owing to similarity to √PER half” (PE17/173). Indeed, in this period like in the 1930s, all the actual derivatives (in both Quenya and Sindarin) seem to be based on √PEND-, so it may be easier to assume that this was the true form of the root.