AllegroTrans Sep 13, 2022:

Yes Tony and Jennifer have explained this well

Yvonne Gallagher Sep 12, 2022:

With Tony And why it is so important that a professional native teacher devises the exercises and is fully confident about the correct answer

Jennifer Levey Sep 12, 2022:

It's context-dependent Contrary to what Nelly's link from https://dictionary.cambridge.org would have us believe, have got and have usually do not mean the same.

Either of the options mentioned by Asker may be correct, depending on the intended meaning, and considered in the appropriate context.

In the absence of context, Do you have lunch at home? will normally be understood as a question designed to discover whether the respondent usually has lunch at home.

In contrast, Have you got lunch at home? is a question about the respondent's luncheon arrangements for today - and also suggests that the question was asked before lunchtime. A similar question asked in the afternoon, would be Did you get/have lunch at home?.

And here's a couple of questions for Asker: Are those the only two options offered in the exercise? If not, what other options were available?

Tony M Sep 12, 2022:

@ Asker That answer would not be wrong, but would express a slightly different — and it has to be said, much less common — idea.
"Have you got lunch at home?" could mean "Oh, you don't want to eat now, as you have lunch already prepared for you at home"
It could also mean "Do you have anything at home you can eat for lunch, or would you like to eat here?"
And finally, 'have you got..." can sometimes indicate a commitent of some kind: "Have you got choir practice this week?" — in other wods, "maybe that's why you don't want to have lunch with me now, as you are planning to have lunch at home"
But none of these is really appropriate for what would appear to be your learners here!
This is a good example of why devising exercises is actually quite hard, to make sure that they are so worded as to actually elicit the desired correct response!