The word ᴱN. amrent or amrint “lark” appeared in Early Noldorin Word-lists of the 1920s (PE13/137, 159), and the word amrint “lark” also appeared in the Gnomish Lexicon and Gnomish Lexicon Slips of the 1910s (GL/19; PE13/110), though in the Gnomish Lexicon the word was initially glossed “robin” (GL/19).
Possible Etymology: The etymology of this word isn’t entirely clear. When glossed “robin”, its initial element seems to have been G. am “breast” and hence probably = “red breast” with its second element a variant of G. crintha “rosy, pink”. When the word was changed to amrint “lark”, Tolkien marked this new entry with a “✱”, indicating it was part of its own derivational group rather than related to G. am “breast”. In the Gnomish Lexicon Slips Tolkien gave its primitive form as ᴱ✶ambarinþǝ (PE13/110) and in the Noldorin Dictionary of the 1920s Tolkien gaves its Qenya equivalent as ᴱQ. ambarin(d-). That document also had the new form ᴱN. amrent indicating some kind of a-affection. It is conceivable that the initial element might be ᴱ√AM(U) “up”, but that seems unlikely since the lark is a ground bird.
Neo-Sindarin: I would adapt ᴺS. amrent “lark” for purposes of Neo-Sindarin, and assume it is derived from ✱ambarint(h)a of now-obscure meaning.
A word appearing as ᴱN. amoth “shoulder” in Early Noldorin Word-lists of 1920s derived from ᴱ✶a-mbod-t’ (PE13/137, 159) and related to ᴱN. bost “back” (PE13/139). In these documents amoth was an element in the name ᴱN. Egallmoth “He of the Wide Shoulders” with an initial element of ᴱN. egall “very broad” (PE13/142, PE13/159).
In the Gnomish Lexicon of the 1910s, the name G. Egalmoth was glossed “Broad-back” and it contained G. alm “back, shoulders” from primitive ᴱ✶alđam- (GL/19), while in Gnomish Lexicon slips modifying this document, the word for “a shoulder” was G. {awlan >>} alan derived from ᴱ✶aldǝmā (PE13/109). These 1910s words were probably based on the early root ᴱ√ALA “spread”, from which ᴱQ. almo or aldamo “back, shoulders” was derived (QL/29).
In Tolkien’s later writings, S. Egalmoth was given an entirely new etymology as “Pointed Helm-crest” (WJ/318).
Neo-Sindarin: Despite the change in the meaning if Egalmoth, I think ᴺS. amoth “shoulder” can be retained for purposes of Neo-Sindarin, reconceived as a derivative of √AM “up” (< ✱ammots-) and perhaps originally an augmentative using the suffix -oth = “✱most up (part of the torso)”.