The problem of evil is viewed from the nation’s perspective. There is no indication that the nation deserved its punishment. Therefore, God’s reputation is at stake—at least, this is how the psalmist unwittingly expresses it.
The occasion of this lament could be the first true religious persecution in history—under Antiochus Epiphanes in 167 B.C.—but overall, the arguments favor the destruction of Jerusalem by the Babylonians in 586 B.C. However, naturally, the psalmist describes the ruin of the Temple: it should prompt God to act if his own house has been attacked. The psalm is unfortunately very relevant today: we pray for the Church of Silence.
But salvation is near. The tears of Jesus over Jerusalem (cf. Lk 19:41-44) connect this lament to his death, even though He said that not a stone would be left unturned from the Temple (cf. Mt 24:2). The destroyed Temple was rebuilt on the third day (cf. Mt 26:61; Acts 6:14). Now, it is greater and more perfect than the old Temple, since it has been raised by God (Heb 9:12). Jesus might weep for humanity today. The weapons of destruction are no longer the axe and hammer, but could be, for example, some current economic systems. All of humanity is called to enter the new Temple. Why not pray with this psalm?