Outside of God's covering and love, there will never be any good for our lives. Acting in disobedience to God will lead us into the captivity of suffering and pain. This is precisely what happened to the people of Israel when they were taken captive to Babylon. The people gave themselves over to idolatry and stopped loving and serving God to worship the images of the pagan gods of the other nations. Faced with this situation, God delivered them into the hands of the king of Babylon and they led a life of mourning and sadness in captivity, far from the land that God had given them as a blessing, "Jerusalem."

Psalm 137 records the laments and sorrow of the people of Israel in captivity.
When we turn away from God we are overwhelmed by lamentation, sadness and despair.

By the rivers of Babylon,
there we sit, and even we weep,
Remembering Zion.
2 Upon the willows in the midst of her
We hang our harps. Psalms 137: 1-2 Reina-Valera 1960 (RVR1960)

Undoubtedly, when we lose a blessing, we feel very sad and we do not stop lamenting. Losing something of value and very appreciated fills us with nostalgia and many memories.
The people of Israel for their disobedience and idolatry lost God's protection and for 70 years lost the blessing of the land that God had given them as He had promised to Abraham, Isaac and Jacob. The people did not value what God had given them and much less did they esteem and value God's love for them. When they found themselves in the land of captivity, they began to weep and mourn for having left the land of blessing, like Jerusalem.

We have to learn to value, esteem, appreciate and love God first and then the blessings that come from God. When we are empty of heart and filled with sadness for the absence of God, it does not cause us to sing. This was what happened to Israel in captivity, it did not provoke them to sing in a foreign land, much less to play stringed instruments. Lament leads us to abandon the praise of God. The people were on the banks of the rivers of Babylon and could not sing to God, but wept and wailed.

Outside of God there is nothing good for our lives, only a deserted life of lamentation and abundant sadness without singing or musical instruments.

It is very difficult to sing when you are full of sadness and regret. If someone asks you to sing when you are going through a very difficult time, you will surely tell them that you can't or don't feel like singing. This happened with the captives of Israel in Babylon, the same people who took them captive, asked them to sing and encourage them. The people of Israel, in the midst of their pain and sorrow, told them that they could not sing. This seemed a mockery, however, it is a consequence of neglect and abandonment to the service of God.

It is difficult to sing and make others happy, when inside you there is pain or suffering.

And those who had taken us captive asked us to sing,
and those who had desolated us asked us for joy, saying:
Sing us some of the songs of Zion.
4 How are we to sing the song of the Lord
in a land of strangers? Psalm 137: 3-4

Israel in captivity kept thinking about and remembering the land of Jerusalem. The glorious land of blessing that God had given them echoed in the mind and heart of every Hebrew in captivity. They longed to be in Jerusalem to sing again and play the musical instruments in praise of God. The people had entered into a wave of repentance and lamentation.

If I forget you, O Jerusalem,
may my right hand lose its dexterity.
6 Let my tongue cleave to the roof of my mouth,
if I do not remember you;
If I do not exalt Jerusalem
as the chief of my joys. Psalm 137: 5-6

In their lamentation and sorrow, the people of Israel called upon God and asked Him to give the just payment of punishment to the people who mocked them when they were taken captive to Babylon and in the same way, they asked God to give the same payment in punishment to the people of Babylon for what they had done to them.
There are times, when in our prayers we ask God for punishment for our enemies, however, God knows the things that others plan evil against us and in due time, God will bring the same evil upon them. In the heart of the people of Israel was the request for vengeance against all their enemies. God will always give just recompense to our adversaries.

O Lord, remember against the children of Edom the day of Jerusalem,
when they said: Raze it, raze it to the ground.
even to the foundations.
8 Daughter of Babylon the desolate,
Blessed be he who gives you a reward
for what you have done to us.
9 Blessed is he who takes and dashes your children against the rock.
against the rock. Psalm 137: 7-9