#effírië noun "death" (isolated from effíriemmo "of our death"). A verbal stem *effir- "expire, die" seems to be implied. (VT43:34)
Is that a compound of the prefix et- and the verb fir-?
Most probably. Quite a literal translation of Latin ex+spirare -> expire.
Well, one can also say "breathe out" in English. And that's not just Latin, but part of many other European (admittedly Latin-based) languages too; The French "expirer", the Spanish "espirar" and "exhalar", the Italian "Expirare", Portuguese Exalar/Expirar, but also the unlatin German "ausatmen" (aus is the German ex). A Pretty international phrase, but I also wonder that Tolkien used it such literal.