While it’s not directly-related to this news item, I was reading the text, and the next news item in the CNN feed on the conflict has Iran warning Israel that it cannot attack Iranian diplomatic facilities, as they are inviolate. That caught my eye:

Iravani also “strongly” warned against “any attack on [Iran’s] diplomatic premises and representatives in violation of the foundational principle of the inviolability of diplomatic and consular premises.”

I think, from memory of reading the Vienna Convention for some other conflict, that that’s not an obligation on parties other than the host state. The host state (the Lebanese government) commits to not entering Iranian diplomatic facilities when it permits establishment of same, but I don’t believe that other countries hold any obligations towards Iranian diplomatic facilities in Lebanon.

kagis

https://legal.un.org/ilc/texts/instruments/english/conventions/9_1_1961.pdf

Article 22

1. The premises of the mission shall be inviolable. The agents of the receiving State may not enter them, except with the consent of the head of the mission.

2. The receiving State is under a special duty to take all appropriate steps to protect the premises of the mission against any intrusion or damage and to prevent any disturbance of the peace of the mission or impairment of its dignity.

3. The premises of the mission, their furnishings and other property thereon and the means of transport of the mission shall be immune from search, requisition, attachment or execution.

kagis more

This Reddit comment from several months back does seem to agree, and is talking about this conflict:

https://old.reddit.com/r/internationallaw/comments/1btv5f7/embassy_protections_in_war/kxpg19y/

First of consulates and embassies are protected under different Vienna conventions, respectively the Vienna convention on Consular Relations of 1963 and the Vienna convention on diplomatic relations of 1961. They confer broadly similar, but not identical, protection to embassies and consular premises.

Both of theses conventions confer on the receiving state an obligation to protect the embassies and consular premises cf. on diplomatic relations art.22 and 45(a), on consular relations 27(a) and 59, but impose no duty on any third party to protect or respect these premises.

Therefore Israel has no obligations towards the Iranian embassy/consulates other than those conferred generally to civilian objects under Jus ad bellum and IHL. Neither IHL nor Jus ad bellum has any special protection of embassies or diplomats.

Regarding locations in third countries it would be a violation of the sovereignty of the third country to conduct millitary operations on their territory (definition of aggression (A/RES/3314, as reflecting customary law art.3(b)). An embassy could be a legal millitary target under IHL, but attacking it would constitute a violation of the sovereignty of the third country.

On the other hand allowing your country, including embassies on your territory, to be used for acts harmful to a country, outside of those acts generally accepted under under customary law applicable to neutral states, would be a violation of the sovereignty of the country injured. Those two countries have a duty to peacefully resolve that conflict and not resort to armed conflict. It could, if severe enough, constitute aggression on the part of the state hosting the embassy cf. A/RES/3314, as reflecting customary law art.3(g and f).

Israel would be obligated to not violate Iran’s embassy in Israel, though (though I doubt that those two have diplomatic relations).

kagis

Yeah, looks like they don’t have diplomatic relations:

https://en.wikipedia.org/wiki/Foreign_relations_of_Iran

Following the Iranian Revolution in 1979, the two states become hostile and the current Iranian government does not recognize the existence of Israel. The back covers of Iranian passports read: “The holder of this passport is not entitled to travel to occupied Palestine”. Both countries have severed their diplomatic and commercial ties with each other. Iran does not recognize Israel and refers to it as a Zionist entity or a Zionist regime.

So the Iranian-embassy-in-Israel situation probably wouldn’t come up; no Iranian embassy in Israel for it to affect.

That being said, if Israel were to hit Iranian diplomatic facilities in Lebanon, it’d presumably tick Iran off, but I don’t believe that it’s an issue from an international law standpoint; it’d be like any other building in war.