You will pursue them in anger and exterminate them from under Your heavens, O LORD.
He first asks God to persecute them in wrath, that is, to be implacable to them; for persecution is, when God not only chastises the wicked for a short time, but when he adds evils to evils, and accumulates them until they perish.
We may observe throughout this chapter a struggle in the prophet's breast between sense and faith, fear and hope; he complains and then comforts himself, yet drops his comforts and returns again to his complaints, as Psa 42:1-11. But, as there, so here, faith gets the last word and comes off a conqueror; for in these verses he concludes with some comfort.
Commenting on Lamentations 3:55-66
from under . . . heavens of . . . Lord--destroy them so that it may be seen everywhere under heaven that thou sittest above as Judge of the world. Next: Lamentations Chapter 4