He can appeal the conviction on the second count, but the scope of the issues he can raise in that appeal is limited by what he pleaded guilty to.
Here is a blog written by a retired Judge of the Air Force Court of Appeals. As the judge writes, "For those unfamiliar with the court-martial process: to plead guilty, a military accused must enter into a colloquy with the military judge in which the judge explains the elements of each offense and the legal definitions that accompany it. See United States v. Care, 40 C.M.R. 247 (C.M.A. 1969). The accused has an opportunity to discuss the elements and the definitions with the judge, who must be satisfied that the accused understands them before accepting his plea. The accused must also describe under oath the acts he committed that give rise to his plea, so that the judge is satisfied that he is, in fact, guilty. If the accused makes statements or offers evidence inconsistent with his plea, it cannot be accepted, and the military judge must reopen the discussion with the accused (formally referred to as a “providency inquiry” or more often and informally known as a ”Care inquiry”) to resolve the inconsistency; or, if it cannot be resolved, reject the plea and enter a not guilty plea on his behalf. UCMJ Article 45(a). Per press reports, it appears LTC Lakin entered guilty pleas to three of the specifications of Charge II. For those pleas to be accepted, he would have to explicitly admit that the orders he received were lawful orders which he had a duty to obey."
So Lakin has already admitted that his superiors' orders were valid; he cannot raise that issue on appeal, even on the second count.
Hold up... he pled guilty to “...pleaded guilty to not meeting with a superior when ordered to do so and not showing up at Fort Campbell in Kentucky where he was supposed to report.”
This seems to me to have a LOT of wiggle room in it.
I think this pleading was very carefully worded for appeal.