The StackOverflow blog post containing details on the introduction of these badges, is here.
As the writer Jon says,
These badges reward reversing the score of a negative question by answering it in a way that sheds new, positive light on the question, raising its score. It’s an answer so good it makes the question look good by association!
I just had a look at the questions on which the Lifeboat badges were earned. See here for that page.
For example, see Why is $\pi$ irrational if it is represented as $c/d$?, where a question concerning an elementary doubt(and why not : the OP was $12$ when he asked it) received downvotes (I would like to hazard a guess that people thought the answer was silly and hence downvoted, as the comments there say), but was rescued or swayed by the answer. That, I think is the right use of the badge, it was awarded to a question that chose to elevate the question to a higher importance with a good answer.
Similarly, most questions which had answers that were awarded this badge, were "diamonds in the rough", which is what Jon intended them to be, prior to the answer being posted.
With this in mind, I would like to think that the lifeboat badge is well merited, because it is awarded to questions which are following site standards but are misunderstood or undervalued by the community, and each of the answers is worth the reputation it got. Therefore, the lifeboat badge is a badge which is earned through effort, and not by answering a bad quality question in typical fashion.
I would like to point out at this stage, that these misunderstood/undervalued questions are often "broader" (non-specific) in nature, so as to provoke deeper discussion and allow for multiple viewpoints (including the "new light" viewpoint), or are well-written with thought-provoking conclusions, thereby stimulating discussion.They meet the standards of the site, and in fact elevate the level of discussion as well, so are worth keeping. The OPs of these questions have also participated in discussions. These questions were worth answering. OP of this meta question had asked if the Lifeboat badge was provoking people to answer bad questions : no, I don't think so.
We move to the Lifejacket badge. I attach the page of awardees of this badge here.
Here, one sees that the last five questions which contained answers awarded the badge, are closed for not meeting MSE standards, for lack of context or for being duplicates. What one notices is that these questions are more specific, and more PSQ like (go through like $20$ of them to see this), but it is obvious from their closure that standards are off. Now, a question like this , it can be debated if it is a "diamond in the rough". Is this a diamond in the rough?
The point I am making is this : if a good answer worth the badge comes, the resulting question should be up voted because the OP realizes that it is getting attention so must get it to meet basic standards : there should be subsequent improvement in the quality of the question, something that is not seen.
I would like to say that in this case, the answers are not always showing the most effort(some of them are not even that long or tedious) but because they are comprehensible to a large audience, the question gets the attention even if it is not good quality, and the answers get upvoted. Examples include here (where the question doesn't have the best quality, and the answers do not "polish a rough diamond" in the least) and here(same).
Basically, these questions were not downvoted because they were misunderstood : they did not follow standards. The fact that a user can elevate such a question by answering it (and that too, not that well) is definitely a sign that people could use this badge as motivation to answer bad questions.
But I don't think they do : they answer the question because (at the first level of thought, and going no deeper) they know the answer to it and want the reputation they get from it, not because they want that badge.
There are only $278$ awardees of this badge. In contrast , how many poor questions in a day get ordinary answers which are upvoted, taking the question up along with them, simply because they are understood by a large audience? Users wanting reputation answer these poor quality questions with bare minimum answers,knowing that the OP will give them an upvote and accept, and other users who just like the question and the answer will chime in (on both Q and A), cancelling out any downvotes received for poor quality. I am not sure the badge is motivating them.
On the other hand, there are good questions as well, those of the kind we saw in the Lifeboat page, like this (good question of effort concerning an elementary topic which was probably scatter downvoted, and comprehensive) and this (good question if slightly vague and misunderstood, but again a comprehensive answer).
So, simply because of the low number of awardees, I am going to say that this badge is not necessarily motivation for anybody to answer a low quality question. However, it could do with a little pruning, probably a little modification which ensures that only those answers are rewarded, which answer questions which subsequently meet MSE standards, after productive edits and/or OP participation.
Of course, if these requirements are too ideal, my take is that the Lifejacket badge issue is slightly being blown out of proportion at the moment, and evidence is too little to make conclusions. However, if this badge ever sees $1000$ awardees consisting of $600$ closed questions (or whatever C.I. someone proposes), I would not rule out the kind of behavior OP proposes!
