There should be a lesson learned from this: What you say, and what another person hears, are not the same thing. Being obsessed with "politeness" can create more problems than it solved.
A asks B if they want to join A for lunch. Case 1 how to get it wrong: B is really, really busy and says "Sorry, I'd love to join you, but I'm really busy". A hears "Go away, I don't want to have lunch with you, and I'm sure you will see through my silly excuse and not bother me again". A thinks "You stupid b (followed by some *** depending on gender), I'll pay you back for that".
Case 2 how to get it wrong: B really doesn't want lunch with A, tries to be polite and says "Sorry, I'd love to join you, but I'm really busy". A hears "I would love to join you for lunch, but unfortunately I have so much work to do, I can't. Please ask me again tomorrow". A thinks "I feel so sorry for that poor xxx (depending on gender), I will ask her tomorrow again to make them feel better".
Assumptions about what other people mean when they say things can create bad situations. Especially when the assumptions are wrong. As a rule, men will tend to take things that are said more literally then women, and they tend to mean what they say more literally. So if you are a woman talking to a man, and you think that what you say is ignored, then examine carefully what the words are that you said, and what it was that you meant to convey, and if these are not the same, then use the exact words that express what you mean. (If you are a man talking to a woman, and you have the impression she thinks you are rude, you might want to change what you say in the opposite direction).
As in this case: The poster didn't want to go to lunch with some man (and of course she is perfectly entitled to that). What she meant to say was "I do not want to go to lunch with you". What she said was "Sorry, I cannot go to lunch because... " in order to be polite.
The result of the attempt to be polite was that the man turned into a harrasser, almost a sex fiend, in her eyes, that she was afraid that he might become her enemy, that she went out of her way to keep a distance from him, and she was ready to report him to HR. Finally, at last, she used words that matched what she meant, and the problem instantly disappeared in thin air.
Put yourself into the shoes of the other person, think how their brain works (it doesn't work like yours), and pick words that are appropriate for that person. In this case, a lot of upset could have been avoided. In the future, someone's career could take off or be cut short, depending on whether other people understand the meaning of what this person says.