I'm not aware of anything in US history that is substantially similar to the Awlaki drone strike, but there was at least one landmark case where a US citizen was hung after being convicted by a military tribunal of violations of the laws of war.

If you haven't already, you should research both Ex Parte Milligan and Ex Parte Quirin. Milligan was a civilian US citizen during the Civil War who was tried, convicted, and sentenced to death by a military tribunal for conspiring to aid the confederacy. The Supreme Court overturned that decision holding that a US citizen cannot be tried by a military tribunal when the regular Article III courts are open. In ex Parte Quirin, eight Nazi saboteurs (including two US citizens) were tried, convicted, and sentenced to death by military tribunal for violations of laws of war. Unlike in Milligan, the Supreme Court held that trial by military tribunal was appropriate, even for the two US citizens. One of the US citizens was put to death, and the other's death sentence was commuted to life imprisonment by Roosevelt because he had assisted law enforcement.

I think Reid v. Covert may also be relevant, but I can't remember if the defendant was originally sentenced to death by the military tribunal. In that case a US citizen murdered her husband on a US military base in England. She was tried by military tribunal under a treaty between the US and Great Britain conferring jurisdiction to the military for any crimes committed by US servicemen or their dependents on the military base. The Supreme Court held that the defendant's right to a jury trial could not be superseded by the treaty.

So, I think Quirin is the only example where a US citizen was lawfully killed without a jury trial; however, he was absolutely given more due process than al-Awlaki. Also, it's unclear (to me at least) how to make sense of the SCOTUS's seemingly opposite rulings in Milligan and Quirin, but it helps to compare and contrast the facts: Milligan dealt with a civilian US citizen, and Quirin dealt with US citizen enlisted soldiers of Germany; Milligan denied conspiring with the enemy and the US citizens in Quirin confessed to their crimes; Milligan was more of a case dealing with domestic terrorism and aiding the enemy, and Quirin dealt more with violations of the laws of war.

Source: National Security Law by Dycus, Berney, Banks, and Raven-Hansen.

May be a bit of a long shot but consider this. Nothing like a drone strike but for instance the US in the early 30,s started Eugenics and Syphilis programs. The first predates Nazi Germany eugenics program and the second is the so called Tuskegee experiment where groups of African American population were lied to and infected with syphilis to study the evolution of the disease.

Now both may be different to what you're looking for but one more direct and the other one in the long run must have resulted in the death of American citizens.

Both are the wikipedia articles for easiness but both cases are well documented and contrary to others there is a wealth of bibliography and references and external links in both articles.

http://en.wikipedia.org/wiki/Eugenics_in_the_United_States

http://en.wikipedia.org/wiki/Tuskegee_syphilis_experiment

As /u/BeondTheGrave points out it has to do with the definition of killing, either a sort of military action as you refer to in the drone example or something rather different as I suggest in my post, at any rate the question is really interesting and is complex.