The correct option is A be able to
Let’s examine the sentence: “Will you ____ have lunch with us tomorrow?” The sentence is in the form of question about future. The question is asking about the ability of the person to ‘have lunch with us tomorrow.’ Hence, the blank needs a word or phrase to express ‘ability.’ The phrase that accomplishes this purpose is ‘be able to’ and it can be used with all the tenses. Hence, Option A is the correct answer. Other options cannot be used as they would make the sentence grammatically incorrect.