I’m not super familiar with this area of law, but according to our government you may lose your citizenship if you commit an act of treason. See: https://www.usa.gov/renounce-lose-citizenship
Treason is defined in the Constitution (and in statute law) in a way that precludes conviction for treason except upon confession in open court, or on the testimony of two witnesses to the same overt act. Treason can't be proved merely by the executive branch deciding you've committed it. The loss of citizenship would only happen upon conviction by a court martial or by a court of competent jurisdiction, according to the statute.
Additionally, technically there are two other requirements before committing treason causes a loss of citizenship, just as with all the other potentially expatriating acts: the treason must be committed voluntarily and with the intent to relinquish citizenship, as judged on a preponderance of the evidence standard (i.e. more likely than not). This is a court proceeding and the claimed loss of citizenship can be challenged, though of course those requirements are more likely to be satisfied in treason cases than in some of the other potentially expatriating acts.
None of this is consistent with a unilateral military strike.
You'd need to be convicted of an act of reason with due process, which would require a court, which would imperil state secrets.
It's much easier to kill you and then say that you and your estate have no standing to challenge the official story to see if you were on a list because only people who know they are in the list can see if they're on the list.
> but according to our government you may lose your citizenship if you commit an act of treason
If you read the applicable provision of law—8 USC Sec. 1481(a)(7)—you have to not only commit an act of treason, but do so “with the intention of relinquishing United States nationality” in order to lose citizenship.
As long as you still want to be an American, albeit a traitorous one, you don't lose your citizenship just for being a traitor.
(And, it also requires conviction of the treason by a court martial or competent court, so if the government wants to give effect to this, it literally not only have to get a hold of the person, try and convict them of treason, and then prove additionally the intent to relinquish citizenship. At which point the last bit is quite likely to be moot.)
Edited for grammar