In the Export dialog, you can set Image Resizing to specific pixel dimensions.
Yes, I'm aware of this. But when I put 1366x768 in, the image it produced was 1365x768
(I should have clarified this is LR4, dunno if 5 is different). I think its behavior is that it
chooses the largest image within those numbers, but with the given aspect ratio, and it
is rounding off the aspect ratio in the wrong direction (for my purposes).
However, as I was writing this, I discovered a silly but doable workaround -- if instead
I enter 1366x769 (or presumably 1366xanything bigger than 768), it will output an image