אֲדֹנָ֥י יִשְׂחַק־לֹ֑ו כִּֽי־רָ֝אָ֗ה כִּֽי־יָבֹ֥א יֹומֹֽו׃
(Psalm 37:13, BHS2003)
The Lord laughs at him,
for He knows that his day will come.
(Psalm 37:13, JPS1985)
The lexical meaning of שׂחק (laugh) in the Qal:
שׂחק: by-form of צחק (with צ for שׂ, see Brockelmann Grundriss §55dα); ...
qal: pf. שָׂחַק, שָׂחֲקוּ; impf. יִשְׂחַק/חָֽק, (וַ)תִּשְׂחַק, תִּשְׂחַק/חָֽק, אֶשְׂחַק/חָֽק, יִשְׂחָֽקוּ; inf. cs. שְׂחוֹק.
—1. to laugh: ...
—2. to amuse, entertain with jokes, serve as a joker Ju 16:27.
—3. שחק ל with both these meanings in Sir 13:6 to joke with, 1311 to laugh at (Smend), 473 to mock, ridicule. †
Koehler, L., Baumgartner, W., Richardson, M. E. J., & Stamm, J. J. (1994–2000). In The Hebrew and Aramaic lexicon of the Old Testament (electronic ed., p. 1315). E.J. Brill.
The picture here isn't God laughing at the wicked's destruction. It is laughing at their schemes in which the wicked believe they can outwit God. The picture is that God isn't threatened at all because His plans will succeed. The wicked's plans are futile.
יָבֹ֥א יֹומֹֽו -- "his day will come" could mean the day of the wicked, but it might make more sense that it means the Day of the LORD (Isa. 13:6,9; Joel 1:15; 2:1,11; 3:4; 4:14; Amos 5:18,20; Oba. 15; Zeph. 1:7,14; Mal. 3:23). In either case God knows the future which cannot be thwarted.
We have difficulty understanding that God knows the future, yet God gives us opportunities to make responsible decisions. As far as humor, we see that when Moses complained to God about the children of Israel, and God tells Moses to step aside while he destroys them, knowing very well how Moses will react but showing Moses the futility of his complaint.
The wicked plot against the righteous, but the Lord laughs at them (vv. 12–13). We do not often think of the Lord laughing, especially at wickedness, and it is right we do not since to us laughter usually means that someone is taking a matter lightly. The laughter in verse 13 is like that of Psalm 2, which says that the Lord “scoffs” at those who think they are able to overthrow him and thus determine their own rebellious destinies. God laughs at the wicked scornfully, because he knows their appointed ends. He knows they will be brought low and be judged by him.
If God can laugh at the wicked, shouldn’t we be able at least to refrain from being agitated by them? Shouldn’t we be able to trust God and commit our ways to him in quiet confidence?
Boice, J. M. (2005). Psalms 1–41: An Expositional Commentary (p. 320). Baker Books.