Article 84 is regarding unlawful enlistment... and therefore not applicable to this situation.
Article 15 is the article that allows for non-judicial punishment - it is NOT something you can be charged with.
Article 91: Insubordinate conduct toward a non-commissioned officer (you failed to obey the order).
Article 92: Failure to Obey a Lawful Order (he ordered you to tell the truth, and you didn't).
Article 107: False Official Statements (told a lie when asked).
Article 134: Disloyal Statements (prejudicial to the good order and discipline)
Article 134: False Swearing (you took an oath and then lied)
Article 134: Obstructing Justice (you lied to hide wrongdoing)
The max punishments you can be hit with are as follows (in the same order!!)
Article 91: BCD, 1 year confinement, forfeiture of all pay and allowances (willfully disobeying an NCO's order), BCD, 6 month confinement, forfeiture of all pay and allowances (for showing contempt to the NCO)
Article 92: Dishonorable discharge, 2 years confinement, forfeiture of all pay and allowances (if the situation involved a general order). BCD 6 month confinement, forfeiture of all pay and allowances (for the failure to tell the NCO the truth).
Article 107: 5 years confinement, forfeiture of all pay and allowances.
Article 134 (statements): 3 years confinement, forfeiture of all pay and allowances.
Article 134 (swearing): Dishonorable Discharge, 3 year confinement, forfeiture of all pay and allowances.
Article 134 (obstructing): Dishonorable Discharge, 5 year confinement, forfeiture of all pay and allowances.
And it depends entirely upon what it was that you are being accused of lying about and the Commander. If it was important, or really impacted Good Order and Discipline, you'll be charged with the maximum number of charges. If it is bad enough situation to warrant an Article 15 you are going to get