Translation:The soup is not on the menu.
Does this refer to the soup not being listed on the menu, or that there is no soup physically on the menu (i.e. soup was not spilled on it, or something)? Could it be both?
Could be both, but the former is the most likely. In order to make clear that the soup is on top of the menu, you could say "De soep staat bovenop het menu." or the other way around: "Het menu ligt onder de soep." :)
If the former is more likely, would it not be better rendered in English as There is no soup on the menu?
No, because that would mean there is no soup at all on the menu. Whereas the Dutch sentence says that the soup is not on the menu, so a specific soup (most likely previously mentioned).
The soup is not listed (written) on the menu.
If the soup is spilled on the menu, in my opinion, use the verb "liggen". (Maybe my opinion is wrong).