Thanks for the chance to help. I am an attorney with over 12 years military law
The term "lawful combatant" really stems from the 3rd Geneve Convention (since if you are a combatant, you are entitled to certain protections if you are taken prisoner)
Here is how they define lawful combatants
1. Members of the armed forces
of a Party to the conflict
2. Members of militias not under the command of the armed forces, with the following traits:
a. that of being commanded by a person responsible for his subordinates;
b. that of having a fixed distinctive sign recognizable at a distance;
c. that of carrying arms openly;
d. that of conducting their operations in accordance with the laws and customs of war.
3. Members of regular armed forces who profess allegiance to a government or an authority not recognized by the Detaining Power.
4. Inhabitants of a non-occupied territory, who on the approach of the enemy spontaneously take up arms to resist the invading forces, without having had time to form themselves into regular armed units, provided they carry arms openly and respect the laws and customs of war.
Though as a matter of policy, the US claims to give combatant status to all prisoners (unless, of course, we deem them terrorists...in which case we give them no rights at all...but that is another topic)