A verbal order in an admistrative chain of command is a lawful order. I authorized means not, I am authorizing. It means it's already done. Past tense. Done. No argument. Already.
I doubt that a tweet would suffice. The tweet used the past tense as if describing an act that had already taken place. Is the President allowed to lie in a tweet? Probably.
Some of us remember the so-called Saturday Night Massacre, in which Nixon was forced to immediately accept the resignations of two officials before he found one willing to fire a Special Prosecutor.
If Trump wanted documents immediately declassified and released he has the power to accomplish it within the hour. One must conclude that he doesn't actually want that.