The lolcat came from a problem with the Stack Overflow API.
Is this usage of lolcat generally understood?
The LOLCat in this case refers to this image, which appears on the Chat error page, so (again, in this case), LOLCat means "the error page" that VonC describes by saying it always triggers a "Oops! Something Bad Happened!" in the question you're getting this from.
In the context of Meta Stack Overflow (and probably only there), "seeing a LOLCat" is generally understood to mean "seeing the error page".
On a related note: I've heard our Careers support team mention that a similar thing is actually very helpful for them. When a (non-technical) person calls up the support and says "I'm seeing muppets", that means a similar thing, because the Careers error page shows, well, muppets.
And "I'm seeing muppets" is an easier thing to describe than "I'm seeing the 500 Internal Server Error response page"; particularly for not-so-technical users.
LOLcat has a pretty specific meaning (a picture of a cat with funny text). If the "something funny" were actually a picture of a cat with funny text that was inspired by a problem from the Stack Overflow API, I think you would be generally understood. But if the "something funny" were some sort of rickrolling, for instance, using the term LOLcat would probably be confusing.
Outside Stack Overflow, a lolcat is simply a funny image of cats.
From the Urban Dictionary:
1. lolcat A photo of a cat doing a seemingly-innocuous thing, with large text superimposed.
For some reason, the entry for lolcats has more relevant information:
1. lolcats An internet meme created by the anonymous imageboard 4chan (lol rules 1&2) as Caturday in 2005 or earlier, which was recently stolen by www.icanhascheezburger.com and renamed lolcats. Most of the images currently circulating have been directly ripped without any consent from the board.
Bottom line: people from outside Stack Overflow will assume you’re referring to the Internet meme.