A lot of responses on here seem to be unable to get past the obstacle of the joke creator dying from thinking of the joke. That isn't a real obstacle, since, in theory, the joke could be devised by an AI program.
Also, a lot of responses seem to be unable to get past the obstacle of how a messenger could relay the joke without dying. That also isn't a real obstacle, since the joke could be delivered via an internet message, telegram, video, etc. without human intervention. It's not unreasonable that after AI generates the joke, it could, in an automated fashion, use a bot account to send a private message to the victim via social media, or create a video and post it on youtube, or something of that nature. It is definitely within a computer program's ability to automatically generate videos, and you have probably seen some on youtube without knowing it.
Can a person die from laughing at a joke? Yes. For the most part, this has a lot more to do with the person's overall health and psyche than the contents of the joke itself. But if a joke were gargantuanly hilarious, it might be able to kill many healthy people. It would just have to be a multiple of as funny as a joke that could kill an unhealthy person.
Is a person and/or AI clever enough to construct a joke that is that funny? All I can say to speak to that is that there are already automated systems that make psychological profiles of everybody in America, use AI to formulate memes / rhetoric that would be most persuasive to influencing their opinion, and distribute it through social media using bots. So the same approach would definitely be usable to make automated systems that can make a deep psychological profile on a specific assassination target and formulate jokes that would be highly funny for that person. Even moreso, since said jokes are targetted for that person's unique psychological make-up, it might be lethal only to the target and some other similar people, and therefore might be sub-lethal for most other human messengers that are telling the joke.
Also, circle back to the theory that a lethal joke would kill the writer of the joke itself... if it is such a struggle to construct a joke that is lethal, and if your very best effort is barely sufficient to do the job, then this joke wouldn't be lethal to anyone that is marginally less vulnerable. So, for example, if a human architect of the joke found the joke 20% less funny, then it wouldn't kill them (this is a stretch, since people often find their own jokes funny). But messengers on the other hand... it's very plausible to teach the joke to a messenger in a way that is very unfunny, for example, by repeating the setup hundreds of times before they ever hear the punchline, or by teaching them the joke while under chemical sedation so that their heart rate never gets too high. By the time they're reciting the joke in a live setting, they've already heard the joke under sedation many times, they've rehearsed it in rote fashion, and the joke has gotten boring and routine.