Have lunch=昼食を食べる 「Have a lunch」はあまり言わないと思います。 予約を立てている時に使うかもしれません。 例: Let's have a lunch …
Have lunch: It refers to the general activity of consuming a midday meal. Example: “Do you want to have lunch together today?” Have a lunch (with an adjective): This form is used when adding a descriptor to the word “lunch.” Example: “We had a delicious lunch at the new café.”
"A lunch" in your example (in a business context, anyway) would generally mean "a lunch meeting". In other words, "I am not …
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