An unglossed root ᴱ√MṆGṆ appeared in the Qenya Lexicon of the 1910s with derivatives ᴱQ. mange “grease” and ᴱQ. manya “butter” (QL/62). G. mang “butter” from the contemporaneous Gnomish Lexicon is also almost certainly related (GL/56). In Qenya Word-lists from the 1920s Tolkien gave ᴱQ. mingwe “butter” which may be related (PE16/141).
Neo-Eldarin: For purposes of Neo-Eldarin, I think it is worth positing a root ᴺ√MANGYA to salvage early “butter” words.
A root in the Qenya Lexicon of the 1910s glossed “lacking”, with derivatives ᴱQ. mange “lack, want, shortage” and ᴱQ. manka “few” (QL/59). There are no signs of this root in Tolkien’s later writing, and it may have been replaced by √PEN “lack” in the 1950s and 60s.