Is killing a gentile also forbidden with the לאו of לא תרצח?

Question

Is killing a gentile also forbidden with the לאו of לא תרצח just in terms of this commandment ? And if so, how can it be permissible to go to war against a nation (מלחמת רשות / discretionary war) which involves killing human beings ? As opposed to a מלחמת מצווה, "War by commandment" where G-d explicitly commanded to conquer the nation.

Answer 1

Raavan (12th cent.) writes that the prohibition against murder includes killing non Jews:

ראב"ן בבא קמא

וכ"ש שאסור לגנוב לגוי דלא תגנוב דומיא דלא תרצח ולא תנאף דהוי בין לישראל בין לגוי.

Rambam, on the other hand, writes (Hilkhot Rotseah 1:1) that that particular prohibition only applies to Jews:

כל הורג נפש אדם מישראל--עובר בלא תעשה, שנאמר "לא תרצח"

Additionally, he writes (Rotseah 2:11) that even if one kills a ger toshav he is not punished by the court:

ישראל שהרג גר תושב--אינו נהרג עליו בבית דין, שנאמר "וכי יזיד איש על ריעהו" (שמות כא,יד); ואין צריך לומר שאינו נהרג על הגוי

Nevertheless, it is completely forbidden. Rambam writes (Hilkhot Avodah Zara 10:1) that even if one sees a gentile worshiping idols it is still forbidden to kill him:

אם ראה גוי עובד עבודה זרה ...לאבדו בידו, או לדוחפו לבור, וכיוצא בזה--אסור

The Kessef Mishneh (Rotseah 2:11) cites the Mekhilta that the punishment for killing a gentile will be imposed by God, although not by the courts. The Kessef Mishneh understands that in this vein, Rambam understands the such a killer is liable to death at the hands of heaven, rather than through the court:

הלכה יא [יא] ישראל שהרג גר תושב וכו'. במכילתא וכי יזיד איש על רעהו רעהו להוציא את אחרים ומשמע לרבינו דגר תושב בכלל אחרים כמו שהוא לענין גלות כמו שיתבאר. איסי בן עקיבא אומר קודם מתן תורה היינו מוזהרים על שפיכות דמים לאחר מתן תורה שהוחמרו הוקלו באמת אמרו פטור מדיני ב"ו ודינם מסור לשמים. וזהו שכתב רבינו אינו נהרג עליו בב"ד כלומר אבל בדיני שמים חייב

This is answers the first part of your question, and constitutes my primary answer.

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Regarding the second part of the question, of why a milhemet r'shut doesn't violate this, it should first be noted that murdering Jews is also a violation of lo tirtsah. Nevertheless, it is sometimes permissible to kill Jews, (such as all those who are liable to death by the courts). Similarly, there can be a prohibition to murder gentiles, but a person may not always be forbidden from doing so.

Regarding milhemet r'shut in particular, it should be noted that according to Rambam (Hilkhot Melakhim 6:1) a war may only be initiated after overtures for peace are made. If they accept the 7 Noahide laws, war may not be waged against them:

אין עושין מלחמה עם אדם בעולם, עד שקוראין לו לשלום--אחד מלחמת הרשות, ואחד מלחמת מצוה: שנאמר "כי תקרב אל עיר, להילחם עליה--וקראת אליה, לשלום" (דברים כ,י). אם השלימו, וקיבלו שבע מצוות שנצטוו בני נוח עליהן--אין הורגין מהן נשמה

Answer 2

The consensus seems to be that it's "Lo Sirtzach". This is clearly the view held by the Raavan (Bava Kama 113 (as mentioned before)), the Ramban (on "Lo Sirtzach"), The Sefer Hachinuch (on "Lo Sirtzach"), Rabbeinu Bachaye (Parshas Bishalach)(he doesn't say it straight out, but it can be inferred) and the Meam Loaz (Parshas Yisro). Additionally, the Mechilta says (Mishpatim) that killing a gentile is exempt from death by the courts but receives a heavenly death penalty, which seems to assume that it's "Lo Sirtzach". The Mesech Chochmah (Mishpatim)and Rav Moshe Shternbuch (Teshuvos vihanhagos Chelek 1, the last 2 Teshuvos in Choshen Mishpat) bring this Mechilta down Halacha Limaaseh.

The Meshech Chochma suggests (Parshas Mishpatim (in his 2nd answer)) that the reason why someone who murders a gentile is exempt from the courts is not because it is worse that killing a Jew, but to the contrary. Because, in addition to the murder there is a huge Chillul Hashem as well, the murderer does not even deserve a Kaparah.

In regards to war, Milchemes Harishus must be done based on the Urim Vitumim. Additionally, there is a factor of a "Rodef". By definition, when a war is being fought the enemy wants to kill the other sides soliders, and as such each solider may have the status of a Rodef. This is the context behind the statement "Tov Shebagoyim Taharog" (Yerushalim Kiddushin). While misinterpreted by by the gentiles throughout the centuries, this statement is referring specifically to a time of war, because each solider is considered a Rodef. (See Tosafos Avodah Zarah, and Rambam Hilchos Avodah Zarah).