The man who commands millions in battle usually sit in a nice furnished office far from the Battlefield. It doesn't make any difference whether he is watching a play or not. That is why the United States Secret Service was founded.
The only way that Lincoln's murder would NOT have been an act of War and COULD have been a true assassination would have been if it had been planned by members of his own cabinet and the Radical republicans party as is suspected by many historians because Lincoln did not support the radical Republican ideas of "reconstruction".
There are many forms of killing someone. All killing are Homocide. However some homocides are viewed as being justified such as in wars, in execution as judgement for a crime committed, and in self defence and even as caused in some accidents. If Booth's killed Lincoln was for reasons associated with the Southern Cause then that homocide by defination was NOT an assassination, because it would have been done as an act of War, because as you point out there was no such "Executive order" at that time which by agreement of both combatant parties that the President of either side were sacrosanct.