This word is attested in later writings as an element in the names Methed-en-Glad “End of the Wood” and possibly Methedras “Last Peak” (of the Misty Mountains). The latter name first appeared in Lord of the Rings drafts from the 1940s as N. Methen Amon and Methendol (TI/404), making it likely that methed is a revision from the earlier adjective N. methen (Ety/MET).
This new form likely changed from an adjective to a noun, since -ed/-ad is usually a gerundal suffix in Sindarin (forming nouns from verbs). This word is clearly a noun in the name Methed-en-Glad, and could also be a noun in Methedras (= “Peak of the End?”).
adj. end, final, last. Ai na vedui Dúnadan. Mae g'ovannen. 'Ah! At last, Dúnadan ! Well met !'. m > v after preposition.