Is there any difference between
I am not having a lunch tomorrow.
I am not having lunch tomorrow.
This is a follow up question of : About the use of future tense.
“A lunch” in your example (in a business context, anyway) would generally mean “a lunch meeting”. In other words, “I am not scheduled to meet anyone for lunch tomorrow.”
“Lunch”, by contrast, would simply refer to the meal, or the food you eat in the middle of the day. So: “I’m not going to eat anything tomorrow between morning and evening.”