I think, "He has lunch" is correct
Have lunch 점심을 먹다 아닌가요?
Have lunch는 점심을 갖고있다
입니다, 점심을 먹다는 eat lunch 입니다.
Literally, it can be translated to "the lunch." However, I don't think a native English speaker would ever say that.
You're right, we never say "He eats the lunch". :P
he is eating his lunch랑 he eats lunch가 똑갔는데....
그 점심이면 the lunch 아닌가요?