Q. Does Adon Olam mean “Lord of the world” or “Eternal Lord”?
In Psalm 89:3, olam chesed yibbaneh must denote, “The world is built up by lovingkindness”. This is the way the Aramaic Targum renders the verse, which must be the source of the rabbinic statement, “On three things does the world stand – upon truth, righteousness and peace” (Avot 1:18; compare 1:2).
On the other hand, Kohelet (in 3:11 and elsewhere) used the word as “eternity”.
Later Hebrew uses olam in both senses, each having a separate plural – olamim for eternity and olamot for worlds.
What the author of the hymn Adon Olam had in mind can be deduced from the context.
He says that God ruled “before every creation was made” and will reign “after everything has come to an end”, and all this seems to indicate an intention to allude to His eternity.