Gloss “effírië” by Ardalambion (Helge Fauskanger)

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.