Everyone speaks about the double-language of "nachamu nachamu ami," a question made no less troubling by the Midrash's answer which speaks of a double-nechama for a double-punishment for a double-crime -- surely G-d's punishment is meted out in exact measure to the crime, no more, no less, and certainly not double what is warranted.
The Nesivos in his commentary on Eichah explains the first pasuk, "Eichah yashva badad ha'ir rabasi am" as a double source of distress. Being isolated without friend is objectively painful; being isolated when there once was an "ir rabasi am" is even more painful because of the relative distance from the glory that once was. Similarly, while any transgression is bad, doubly-bad is the transgression of a people who were singled out to be G-d's chosen nation (see the Maharal we discussed here). And perhaps it is these two dimensions which call for a double nechama.
The Shem m'Shmuel has a beautiful insight on the continuation of the haftarah, "Dabru el lev Yerushalayim v'kir'u eileha," where the Navi is told to call to speak to Yerushalayim and call to her. What is the meaning of "calling" to Yerushalayim? Why not just speak the words of nechama? The Avnei Nezer explained the difference between the word "vayikra" used when G-d spoke to Moshe and the word "vayikar" when G-d spoke to Bilam is that vayikra, calling, demands that the listener draw closer to the speaker, while vayikar means that the speaker simply encountered the listener and began his address. Anyone who has done public speaking knows that the first thing you need to do before launching into your message is call for your audience's attention -- issue a keri'ah to them. Speakers like to open with a story, a joke, a question. No matter what promise you deliver and no matter how beneficial what you are selling is to your audience, 'V'lo shamu el Moshe m'kotzer ruach..." unless people are prepared to listen, you can't communicate. The Jewish people in galus have their ears turned off to the positive message of Torah. They need to be called to, they need to be drawn out of their preconceived ideas and notions, and only then will words of nechama and words of Torah make a difference.
The Midrash opens P' VaEschanan: Aba Shaul says, "This is the siman of tefilah -- if a person's heart is attuned to his prayer (kavanas halev), then that prayer will undoubtedly be answered." The Midrash then continues that in Tanach there are ten different expressions which are used for prayer, and the Midrash lists them and offers examples from various pesukim. On the one hand the Midrash depicts prayer as kavanas halev, as rooted in a person's thoughts or heart; on the other hand, there are no less than 10 different ways to describe the external expression which constitutes the act of prayer. Based on the Shem m'Shmuel, there is no contradiction (see also Sefas Emes in the first piece on the parsha): these 10 expressions are the keri'ah to prayer, but are not prayer itself. The words of the siddur are meant to grab our attention, to arouse our feelings, to set the mood for prayer, but prayer itself is not the words uttered, but the feeling of the heart and thoughts of the mind which those words engender.