Adam Clarke on Psalms 137:5

If I forget thee, O Jerusalem - Such conduct would be, in effect, a renunciation of our land a tacit acknowledgment that we were reconciled to our bondage; a concession that we were pleased with our captivity, and could profane holy ordinances by using them as means of sport or pastime to the heathen. No: Jerusalem! we remember thee and thy Divine ordinances: and especially thy King and our God, whose indignation we must bear, because we have sinned against him.

Let my right hand forget - Let me forget the use of my right hand. Let me forget that which is dearest and most profitable to me; and let me lose my skill in the management of my harp, if I ever prostitute it to please the ungodly multitude or the enemies of my Creator!