Albert Barnes Commentary Psalms 53:2

"God looked down from heaven upon the children of men, To see if there were any that did understand, That did seek after God." — Psalms 53:2 (ASV)

God looked down from heaven ... - See the notes at (Psalms 14:2). The only change that occurs in this verse is the substitution of the word אלהים ('Elohiym)—rendered “God,” for “Yahweh,” rendered “Lord”—in (Psalms 14:2). The same change also occurs in (Psalms 14:4) and (Psalms 14:6).

It is to be observed, also, that the word “Yahweh” does not occur in this psalm, but that the term used is uniformly אלהים ('Elohiym)—God. In (Psalms 14:1–7) both terms are found: the word אלהים ('Elohiym) three times (Psalms 14:1–2; Psalms 14:5), and the word יהוה (Yahweh) four times (Psalms 14:2; Psalms 14:4; Psalms 14:6–7).

It is impossible to account for this change. There is nothing in it, however, to indicate anything in regard to the authorship of the psalm or to the time when it was written, for both these words are frequently used by David elsewhere.