No, that's not accurate, at all. This is well-settled law. It's called the de facto officer doctrine and it says "The de facto officer doctrine confers validity upon acts performed by a person acting under the color of official title even though it is later discovered that the legality of that person’s appointment or election to office is deficient.". This doctrine has been incorporated into military law for decades - see: US v. Jette and US v. Watson. Of course, none of this will even be considered by the court because the military judge will rule Obama's eligibility irrelevant. That ruling will be upheld on appeal, easily.
"Since lakin has been charged he already has standing, and can even proceed separately with a Quo Warranto suit in the DC courts. I doubt he will do so."
Obama is neither the issuer of the order that was disobeyed, nor was he the convening authority for Lakin's court-martial. Why would a prerogative writ be granted in such circumstances?
"Since Lakin is the defendant, he has to be proved guilty of disobeying an legal order from a local commander who has the legal authority to give it from the chain of command."
This statement doesn't acknowledge that in a military court of law, orders are presumptively legal. Do you know what presumptively legal means, and how that affects burden of proof? For the government to prove its case, all it has to demonstrate is that Lakin missed a movement, and that he disobeyed an order(s). These are two charges that are proved EASILY.
"The result will depend on the Military Judges and their views of the role of the constitution. If they believe in the constitution as supreme law they sould allow Lakin discovery."
This is how liberals think - they want jurists to ignore statutory law, case law and principles of jurisprudence to arrive at the conclusion that that feel is just, rather than legal. This is not how a competent and conservative trial court works.
But since he is allowed to argue that the order was illegal, and the MCM indicates that a legal order must proceed from someone with the legal authority to issue such an order, the de facto officer doctrine, which is not as straightforward as you potrary it, not even as indicated in the case you cite, would not apply in this instance.
It would apply in cases where someone was accused of performing an act in pursuat of an order later found to be unlawful, or more properly unauthorized, but not obviously illegal in an of itself.