Thank you! Your comment has helped me understand and make better sense of the situation.

When God condemns blood-shedding in Gn. 9.6, it's a command against premeditated murder. It's different from unintentional homicide, self-defense, and war. Humans are supposed to take steps to regulate and contain the rampage of violence and evil on Earth.

In Genesis 14, Abram is righting a wrong. People have been kidnapped to be enslaved. Money and goods have been stolen. He is, in a sense, defending what is his (his nephew and Lot's family).

Why was it okay for Abram to attack and go to war in Genesis 14:15 to save Lot?

I thought it was something bad to kill since in Genesis 9:6 it says, “Whoever sheds the blood of a human, by a human shall that person's blood be shed; for in his own image God made humankind.” ‭ Or was it okay for Abram to defeat those humans since they had gone to war with other humans first and defeated them? ‭