Sorry, I can’t join you for lunch. I will meet my writing supervisor to discuss my dissertation.
These days this kind of meeting is difficult to re-schedule. Academic staff are increasingly busy and the time allowed for consultation increasingly short. If you try to change the time you may lose the opportunity altogether. This plan is fixed. You may have written it down in a diary. if you only made a mental note then that note is burned into your subconscious. It’s an important meeting. In this case you need:
I know, the meeting is due to take place in the future, but when a plan is difficult to change use present continuous tense, especially when you’re excusing yourself from some other offer.
Sorry but I have to go now. I’m teaching a class in 10 minutes!