A scenario I can think of is when you gather your colleagues to go eat lunch outside; "lui ha il pranzo" can be intended as "he has his (boxed) lunch (so he won't come)". The English wording is awkward though, in cases like this you should substitute the article with a possessive.
I agree - English people don't go around saying "He has the lunch" unless they are just trying to be silly. Unless "pranzo" can be translated more vaguely into food, meal etc this does not work. Is it idiomatic perhaps?
How about "He has his lunch"? Not as in "he is eating lunch", but as in "You don't have to worry about giving Billy money for the cafeteria. He has his lunch". I'm thinking that "his" would be implied. What say you, amici Italiani?