Attacking an embassy is against all forms of international law.

Ehhh...actually, I'm not sure that that applies here. The Vienna Convention on Diplomatic Relations definitely requires you to protect consulates in your country, but they hit one in Lebanon. Like, in your country, you get to choose whether or not to permit a diplomatic mission. I don't think that a country can just make something inviolate against someone else's military action by declaring it a diplomatic mission.

googles

Yeah, Article 22 constrains the host state (the "receiving state"), not other states:

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.

Once -- and as long as -- Lebanon recognized the building as a diplomatic mission, then Lebanon became bound to try to prevent attacks on it, regardless of whatever Iran is doing there. However, Israel wouldn't be bound.

The only obligation that Israel has, as a "third state", would apply to not blocking transit of personnel, messages, and diplomatic bags if they have to pass through Israeli territory on their way to and from the consulate:

Article 40

1. If a diplomatic agent passes through or is in the territory of a third State, which has granted him a passport visa if such visa was necessary, while proceeding to take up or to return to his post, or when returning to his own country, the third State shall accord him inviolability and such other immunities as may be required to ensure his transit or return. The same shall apply in the case of any members of his family enjoying privileges or immunities who are accompanying the diplomatic agent, or travelling separately to join him or to return to their country.

2. In circumstances similar to those specified in paragraph 1 of this article, third States shall not hinder the passage of members of the administrative and technical or service staff of a mission, and of members of their families, through their territories.

3. Third States shall accord to official correspondence and other official communications in transit, including messages in code or cipher, the same freedom and protection as is accorded by the receiving State. They shall accord to diplomatic couriers, who have been granted a passport visa if such visa was necessary, and diplomatic bags in transit, the same inviolability and protection as the receiving State is bound to accord.

4. The obligations of third States under paragraphs 1, 2 and 3 of this article shall also apply to the persons mentioned respectively in those paragraphs, and to official communications and diplomatic bags, whose presence in the territory of the third State is due to force majeure.