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Since there is no consensus definition of rationality, there cannot be definitive answers to this type of question.
If you take rationality to be maximising utility, you're still left with questions. Is it individual utility or collective utility? If it's collective utility, what is the scope of the collective: the nation or the globe?
In my opinion, for each of these types of rationality, there are marginal circumstances where lying would be the most rational course of action. It's hard to avoid this fact if you're a consequentialist, and most modern rationalists are.
To take a trivial example, lying could prevent a global catastrophe that would wipe out the human race. Of course, if you take a broader scoped morality, there are likely to be less circumstances in which lying is the rational approach than if you are maximising individual utility, but such circumstances do exist.
If you wanted to go more deeply into it, you would have to consider the fact that individual utility and collective utility are not entirely separate.
No, it's not an April fools joke.
It's a pattern I noticed in myself, and I decided to write it up. Just because we sometimes use thinking about productivity as a means of procrastination, that doesn't mean we should never think about productivity. The note at the end was just a humourous addition, rather than the purpose of the article.