Pakistan, the mediator of the agreement, declared that a ceasefire in Lebanon was part of the agreement when the agreement was announced:

https://www.reuters.com/world/asia-pacific/what-us-iran-isra...

>Pakistani Prime Minister Shehbaz Sharif announced the ceasefire between Iran and the United States on X, saying the two sides agreed to an immediate ceasefire everywhere, including Lebanon, where Israel launched strikes.

This suggests that either the Americans are lying or they did not read the agreement carefully before signing. Either way I don't think it's a good look for the United States.

The US has plenty of ability to force Israel to stop its invasion of Lebanon and it has done similar things twice before by economic means. All parties to the agreement are aware of this.