Your mother's preparing lunch. Even if you are certain you won't eat lunch that's supposed to be ready in two hours, would you prefer to say, "I won't need lunch." over "I don't need lunch." if you had to choose one of them? Could you give me your impressions?
The most gentle and polite way of expressing the idea is to use a future continuous, 'won't be needing'.
"Thanks so much, Mum, but I won't be needing lunch today so don't give yourself unnecessary work. I'm having lunch with my boss, but I will be home for supper".