99.9% of the time, when we talk about eating our midday meal, we say 'have lunch'.
I have lunch in the canteen.
Do you want to have lunch together tomorrow?
I'm hungry because I haven't had lunch yet.
This is the same for all meals - breakfast, lunch, dinner, supper.
The only time when you would say 'a lunch' is when this is a formal occasion or celebration of some kind. For example, you might say:
'We're going to hold a special meal for the CEO's retirement and invite all the company's employees. We'll either have a lunch or a dinner at a nearby hotel.'
But, as you can see, this is a fairly unusual usage.