Everything already said is valuable. By calling his proposal "modest," Swift might have been hoping to entice readers unaware of the horrific nature of the (ironic) proposal he was about to offer. Unsuspecting readers would have been lured into taking the bait ("here's a fellow who may have something useful to offer"), only later discovering the true nature of Swift's suggestions. Half the fun and all of the surprise would have been ruined if Swift had titled the essay "A Truly Sickening and Disgusting Idea about How to Eliminate Starvation in Ireland by Eating Irish Babies." An essay with this kind of title would not have had the intended impact.
I think the persona of the speaker in the essay is something that is worthy of note. The speaker does everything he can to establish himself as a serious, sympathetic and caring individual who genuinely wants to do something to alleviate the problems. In addition, his focus on numbers and other quantifiable facts introduces the way that taking statistics to their extreme can result in horrific conclusions.
It seems your question answers itself. To lampoon something is to criticise it using ridicule or sarcasm. A satire criticises society, a group within society, an individual or a social concept through ridicule or sarcasm. The objective of each is to attain more rational and sound behavior from the public and to restore society--or the criticised element thereof--to the morally socially accept norm. So Swift lampooned his satirical proposal because he was introducing the satirical criticism with which he aimed to lampoon British society and shame it through ridicule and sarcasm back into--or into--more rational, compassionate, humanistic behavior toward the Irish.
Everything Swift discusses in his "Modest Proposal" is big--except his simple little plan. So many rich people fleeing the country is a big problem. Having so many poor people who need help is a big problem. Children begging and stealing unchecked on the streets is a big problem. And the list goes on. His idea, he says, is small; however, it is a sensible one and he simply wants his plan to be considered as reasonably as any other--except there is no other, since so little is being done to alleviate any of these issues. As has already been said, Swift's use of sarcasm and irony to effect change is what makes this work so memorable. There is nothing "modest" about the problems or the plan.
Sarcasm is often employed by writers to instill a specific feeling in the reader. Back in the times where there were no cliff notes, synopses, nor other form of knowing what a novel or play was actually about, people resorted to either reviews, word-to-mouth information, or through leading themselves by the title of the work. Those readers who were fortunate enough to know and predict Swift's style would have guessed that he was up to something when he selected this title for his story. Those who were not familiar with his writing style were in for a huge surprise. Therefore, Swift deliberately choose a sarcastic and ironic title for a story that treated topics that were controversial and socially unacceptable.
By modest, he was suggesting that it was not a big deal. The proposal was minor. This made the point of the satire clearer. Swift's proposal is not at all modest. It's an incredible suggestion. It's also a play on words, a double meaning. Modest can imply that Swift himself is being modest, when the proposal is incredibly conceited.
I agree completely with what the previous post says. When writing satire, people often use irony/sarcasm to get their point across.
Swift is also trying to pretend that his whole project is very normal and that no one could disagree with it. He writes in a way that is meant to project a very reasoned tone. To fit in with this, he calls it a "modest" proposal.
So, Swift uses the word "modest" to heighten the satire by making it sound as if he thinks that his proposal is totally reasonable.
In Jonathan Swift's essay entitled A Modest Proposal, I believe that since the rest of this satire was harsh and outrageous (the darkly satirical idea of eating babies sold to rich people so the poor could survive without resorting to prostitution, thievery, etc.), it probably seemed appropriate to him to point out what an outlandish point he was trying to make—by sarcastically terming it a "modest" proposal...when in fact, it was gargantuan!
His terse mock-treatise A Modest Proposal is considered the most brilliant short prose satire in the English language.
Swift's concern, of course, was to do something about the terrible state of affairs in Ireland that he had witnessed first hand. However, those who are financially secure may not always (or ever) wish to show concern for the the hardships of others. It's not their "revolution." Of course, the title probably did not find significance with the audience until readers understood what Swift was "proposing" because he started the essay out quietly, with control and "gentle concern."
The essay begins innocently by establishing the speaker as a concerned citizen genuinely sympathetic to the Irish poor...
Once Swift gets into the "meat" (pardon the pun) of his argument, the title takes on new meaning.
The modest proposal is of course anything but modest: It is savage, frightening, perhaps even insane.
However, none of it means anything if the audience which it was directed do not get the point. The Irish continued to suffer, and it was something that greatest troubled the civic-minded Swift.