Is the usage (someone) is off for lunch correct?
I think the above usage is right but I am not pretty sure.
Yes, very informal, found mainly in speech/ tweets/ blogs.
Off for lunch = out to lunch.
Note the other errors of grammar, spelling and style showing that it is casual writing.
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Remember that the other expression out to lunch is an idiom that has other connotations as well, and should be used with care!
While off for lunch is not idiomatic in the same way out to lunch is, I can certainly be off for lunch if I am on at other times:
I could also be off to lunch if I'm leaving for lunch.
Off for lunch is correct. Out at lunch is also correct. Out to lunch, not so much. Out to lunch doesn't mean that a person's having a lunch, instead it means, quoting:
Basically, an out to lunch person is someone that's not paying attention.