“In the menu” vs. “on the menu” (in software)

This comes up often, and here's the general answer.

In this specific case, menu can be viewed either physically, printed on paper to read, i.e,

• 2-Dimensional, in which case on is used
  • It's right there on the menu; you can't miss it.

or informationally, like a list, or a report; this a Container metaphor, i.e,

• 3-Dimensional, in which case in is used.
  • It's hard to resist the Armenian dishes in the menu.

Quite often it makes no difference, because the information that's in the menu is also printed on the menu.

This alternation is true of any physical noun that can be interpreted as information, like story, picture, book, article, paper, report, list, plans, etc. These are collectively called "Picture Nouns" and they have very complex syntax in English.

If one wants to ask if a menu contains a given item X, one could use either of "Is X on the menu?" and "Is X in the menu?", but by personal preference I'd incline toward on.

If one wants to ask if a person is sitting atop a menu, one could say "Are you sitting on the menu?" and would not say "Are you sitting in the menu?".

If one wants to ask if someone trapped a fly by closing a restaurant's menu upon it, one could say "Is the fly in the menu?" and would not say "Is the fly on the menu?". The latter would ask (ambiguously) either whether the fly is sitting on the menu or whether the fly is listed on the menu.

You may wish to look up in and on in a dictionary and find out what they mean.

Also see 40-some sentences using in ... menu and a couple hundred using on ... menu, per just-the-word.com. A notable fraction of the in ... menu examples are related to constructing menus for computer applications; I don't know if that is a corpus-related artifact or a true reflection of usage.