I think Luttwak is advocating imitating St. Justinian, Basil II Bulgaroctonis, and the Comnena dynasty, not the Paleologoi—there’s nearly a 1000 years from the retirement of the last Western Augustus to a villa near Naples in 476 to the fall of the Empire in 1453.
The failure of the Empire was occasioned by increased reliance on outside support in its latter days (neglecting the fleet in favor of Genoan mercenaries, for instance) and the treachery of erstwhile allies—the Crusades harmed the Empire far more than they harmed the Muslims, and in the end the walls of Constantinople fell to Hungarian-made cannons.
And Luttwak is advocating imitating the Imperial intelligence services and use of subversion to pit allies against each other, not falling behind times on tactics. The Muslims relied on a precursor to the modern fire-and-movement doctrine to a much greater degree than the Imperial forces did (the elite cataphracts could out-match the Muslims, but they were too few in number, and the bulk of the Imperial legions were not mobile enough and relied too much on close-combat).