Haamek Davar (ad loc.) explains that צלם אלקים (in Genesis 1:26–27) refers to an angel, also called a person's מזל, which envelops each of us and protects him from harm. He (to 4:14) explains further that "ההורג נפש אפי׳ בשגגה אובד צלמו", someone who kills a person, even accidentally, loses that צלם אלקים. Does the same apply to someone who kills a person with permission, or even who is required to do so? (Some examples may include a soldier in battle, a king killing a rebel, an agent of a court executing a criminal, or someone acting in self-defense. But don't get hung up on my examples: I'm asking about any case in which someone was allowed to kill a person.) (On the one hand, he doesn't explicate that such are excluded from his rule; on the other, he only says "בשגגה", by accident; on the third, שגגה, accident was the context there, so maybe he didn't mean to exclude cases like those in asking about. Also, on the one hand, maybe the very act of killing a human is what caused the loss of one's angel; on the other, maybe it's the fault involved; or maybe it's something else.) Knowing what others who hold a killer loses his צלם אלקים or מזל hold about a killer with permission would be satisfactory, since the Haamek Davar author himself may not address the issue.
 I don't quote here his entire commentary to 4:14, but it clarifies that the quotation above is referring to the צלם אלקים as in 1:26–27.