I use big-endian in english, but lojban's specified (I think? I
only remember this from nick/robin's lessons; dunno what, if anything,
the book says) to use little endian.
It's probably not a problem to go ahead using big-endian, though,
since the two are unambig because the year is 4 digits.
I don't think that the book says anything about it, though I'm not
completely certain, but at any rate, this is clearly an extra-linguistic
issue. In the US they use middle-endian dates, whereas in Britain they
use little-endian dates, and no one claims that Americans and Britons
speak different languages because of that. It's a bit like metric vs.
English Imperial.