The Malbim writes that Esther’s two conditions refer to separate factors. The first, “seeing evil” refers to possible anti-Jewish attacks before the decree date. The second, “seeing the destruction” refers to people perhaps not believing the second (erstwhile unmentioned) document, and attacking the Jews nevertheless.
In Nachal Eshkol, the Chida explains that Esther is telling the king that – having not been present during the meeting that spawned Haman’s decree – she does not know if, by using the term li’avdam (Esther 3:9), Achashverosh meant to enslave or kill the Jews. On that basis, can’t bear evil (enslavement) nor the destruction (killing) of the Jews.
The Vilna Gaon notes that the verse uses the word, eicha (“how”) twice – once for the first Beis HaMikdash, and the second for the second Beis HaMikdash. Indeed, Esther was mourning for two things – the potential destruction of the Jews in exile from the first Beis HaMikdash, and the inevitable destruction of the Jews of the future if they do not learn from their past mistakes.
Contrary to the previous opinions, the Yosef Lekach writes that Esther is not worried the people will be destroyed. After all, H-Shem already promised never to kill them out (Vayikra 26:44). However, there was no such promise about individual families, and that was a cause of concern for Esther. The Jewish people would survive, but Esther’s second eicha indicates that she worries about her future progeny surviving.
Perhaps she had good reason to worry, since Mordechai had threatened her offspring with as much when he convinced her to approach the king (Esther 4:14), and it is a well-known Talmudic (Kesubos 103b) dictum that what the righteous speak, H-Shem fulfills.
The Beis HaLevi (on his commentary to Ki Sisa) writes that by using “my nation,” Esther refers to those who would not renounce their Judaism if that is what Achashverosh is planning to do. By saying “my kin,” Esther refers to those people who would (chas v’shalom) give up their Judaism to save their lives.