If you want us to correct this, or want to know if it's a natural expression, please tell us. Don't just write some words and expect us to guess why you have done so.

If you are wanting the sentence to sound correct:
Have you taken your lunch? or
Have you taken a lunch?

AnonymousHave you taken your lunch? or
Have you taken a lunch?

These would sound wrong to most AmE speakers.

Aspara Gus AnonymousHave you taken your lunch? orHave you taken a lunch?These would sound wrong to most AmE speakers.

Right! Have you had your lunch is much more natural. To take a lunch would be to take it from home to work.

PhilipTo take a lunch would be to take it from home to work.

Ah, that interpretation didn’t even cross my mind.

Aspara GusAh, that interpretation didn’t even cross my mind.

Yes, 'to take (your) lunch" means to bring your lunch from home to school or work. But I can't think of a context in which someone would say "have you taken a lunch?" You might say "Do you buy lunch at school or take your lunch?" Sometimes it's called "a sack lunch" because it used to be carried i

khoffI think what the original poster was looking for is "Have you had lunch?" or "Have you eaten lunch?"

Me, too.

I thought I read somewhere that some speakers of BrE used take in the sense “eat”, but my memory could be playing tricks on me.

Aspara GusI thought I read somewhere that some speakers of BrE used take in the sense “eat”, but my memory could be playing tricks on me

It's not playing tricks, but that was only ever used by an upper-class minority. I doubt if anyone still says it today. I sdon't move in those circles, so I can't be sure.

It could be a remnant of the Norman Invasion, because the French do use the verb "to take" rather than "to eat" when talking about having a meal.