That's a bit silly--why would military orders be preserved? Our body of Classical texts is composed almost entirely of stuff that was copied and preserved throughout the Middle Ages, mostly by monks. Why on earth would your friend think that Byzantine monks would give enough of a crap about military orders (which might never have been committed to writing in the first place) to preserve them? For that matter, why would anyone give enough of a shit about them for them to last into late antiquity for Byzantine monks to even get their hands on?

If we're talking about Classical Sparta, no texts whatsoever survive, unless there are some inscriptions about. Plenty of texts talk about the Spartans (though the vast majority of stuff about the Classical Spartans was written much later, in the 2nd Century, AD during the Second Sophistic), but nothing survives from Sparta itself at all from the Classical Period. Our largest body of Spartan writing by far is not composed of military orders at all, it's elegiac poetry from the Archaic poet Tyrtaeus, some of whose fragments are quite substantial. Tyrtaeus' poetry is very martial, but they aren't military orders by any stretch of the imagination, nor do they necessarily represent any sort of militaristic reality in Sparta, but appear to be largely in imitation of epic, somewhat like Archilochus.