The first 4 Perakim of Eicha are written in the order of the Aleph Bais. However in Perek 2, 3, & 4 the Pesukim for פ are written before the Pesukim with the ע. Why? And then why in Perek 1 is it in the correct order?
The Gemara (Sanhedrin 104b) says that it is because peh means "mouth" and ayin means eye, and it therefore symbolizes the sin of the spies, "who said with their mouths [false reports about the Land of Israel] that they did not see with their eyes."
Maharsha there adds that the regular order was retained in the first chapter of Eicha, because otherwise we would think that Yirmiyahu simply had a different ordering of the Hebrew alphabet than we do. (Indeed, some modern scholars claim exactly that.)
Lechem Dim'ah (R. Shmuel de Uceda, a disciple of the Arizal) offers a different reason: in ch. 2 the verse for פ tells of how our non-Jewish enemies gleefully "opened their mouths... hooted and gnashed their teeth," while the ע verse describes Hashem actually carrying out the destruction. In other words, the gentiles began harassing the Jews even ahead of Hashem's granting them license to do so - which in turn was punishment for the spies' sin, as above. Thus, it is appropriate to change the order only beginning here.
Etz Yosef cites Nachalas Binyamin, who says that another reason is because, after all, the spies did start out by speaking the truth - in other words, at first they did put their ayin before their peh. He also cites Alshich, that it is because the צ verse in ch. 1 is King Yoshiyahu's deathbed confession for having disobeyed the word of Hashem's peh, and we don't want to incorrectly imply that he also sinned against Hashem's ayin, which would be implied if they were juxtaposed.
According to this article on Seforimblog: