Who says this?
Radak (6): In these last three verses, the author speaks.
Why does he ask Hashem to remember Bnei Edom?
Malbim: If I constantly remember Yerushalayim and mourn over it, all the more so You, Hashem, should remember for Edom the day of Churban Yerushalayim.
What did Bnei Edom do?
Radak (6): While the author prophesizes about the first Churban, via Ru'ach ha'Kodesh, he saw Churban Bayis Sheni via Edom. Titus, from Malchus Romi (Edom), destroyed it. Also Yirmeyah, while prophesizing about Churban Rishon in Megilas Eichah, he saw Churban Sheni, and said "Sisi v'Simchi Bas Edom" (Eichah 4:21) as a threat. It is like "Semach Bachur b'Yaldusecha" (Koheles 11:9). Eichah Rabah 4:26 says that Bas Edom is Kisari in Eretz Utz, i.e. Romi.
Malbim: They helped 1 to destroy (Yerushalayim).
It seems that Malbim learns from here that Edom helped to destroy Bayis Rishon. Above (1) he said that the Mizmor discusses when Koresh conquered Bavel. He did not say that now it switches to discuss Churban Sheni. Also, Edom did not merely help bring Churban Sheni! (However, perhaps the primary Churban was due to Yisrael's sins, like it says about Churban Rishon (Eichah Rabah 1:41) 'you killed a dead lion; you grinded ground flour...' - PF)
What is "Yom Yerushalayim"?
Radak: It is the day of its Churban.
What is the meaning of "Aru Aru Ad ha'Yesod"?
Rashi: It is an expression of Churban, like "Chomos Bavel ha'Rechavah Ar'er Tis'ar'ar" (Yirmeyah 51:59) and "Aros Yesod" (Chabakuk 3:13). It applies to something uprooted from its roots in the ground.
Radak: Destroy and make fall the building of Yerushalayim, until the foundation is revealed.
