Boyd’s Bible Dictionary:

(destroy not). In title to Psalm 57; 58; 59, 75. Probably the tune is meant.

Concise Bible Dictionary:

Two Hebrew words untranslated in the titles of Psalm 57, Psalm 58, Psalm 59, and Psalm 75, reading in the margin “destroy not,” and thus rendered in the LXX. The general thought is that reference is made to some air to which these Psalms were sung. The words, however, may have been taken from what David said in 1 Samuel 26:99And David said to Abishai, Destroy him not: for who can stretch forth his hand against the Lord's anointed, and be guiltless? (1 Samuel 26:9), “Destroy him not.”

Strong’s Dictionary of Hebrew Words:

from 408 and 7843; Thou must not destroy; probably the opening words to a popular song
KJV Usage:

Jackson’s Dictionary of Scripture Proper Names:

thou mayest not destroy A’lush, I will knead (bread)