You just answered your own question, I think. Tombstone forgive me if I don’t shake hands shirt The lunch lady has a job to do. You happen to be sitting at the table she needs to wipe. She only has so much time to do her job. It has nothing to do with you personally. If she doesn’t get her job done, she’s in trouble. Your reading not being disturbed is not on her list of jobs. The next group of kids coming in need clean tables. As far as what you should do, you are already doing it by moving your arms and being polite. The only other thing you could do is to keep in mind what a thankless, repetitive job she has. Perhaps you could smile and say “thank you, have a nice day.” The difference is subtle, but “I will have my lunch with my lady now” implies that.
I have become available to have lunch with “my lady”, Tombstone forgive me if I don’t shake hands shirt and have determined so to do, whereas “I am going to have lunch with my lady now” is passing on the information as to what I shall be doing for the next hour or so. The first formulation would be more common in other settings, e.g. “we will take questions from the audience now” (permission is given to ask qestions) and its variant “we are going to take questions from the audience now” (the stage in the proceedings that we have reached). Back in middle school 8th grade, they used to have these milk cartons in the cafeteria that they sold for 50¢ each.