Friend wants to change the menu. Which at best tends to upset other people that wanted the orginal menu and were looking forward to it.
You know, my response to those people would be, "suck it up! Your host chooses the menu. Your host is not a restaurant."
This is getting to be at theme--people (like the OP's Weight-Losing Friend; and the friends that made another EHellion stop having dinner parties) who expect to "order" the food as if they are customers!
For the OP, I thought at first the Weight-Losing Friend was simply checking to be able to plan.
But from additioanl info in the OP, and in the update, it's definitely time for this (variations suggested by several people--most recent example snipped):
Then let her wait. Instead say "Oh, I understand. We'll get together another day."
Or, just say, "Well, that's the menu--I know that XYZ is stuff that fits your diet plan. Let me know if you'll be coming--if I don't hear from you by Thursday, I'll assume it's a no."
Like this (except--there's no "compromising"--you are the *host*, and you don't compromise; you of course make menu choices that will be appealing to your guests, so of course you *already* plan some foods she ought to be able to eat, but you don't ask for her to agree with your decisions, especially not when she is already being over the line in terms of unreasonableness and making you feel manipulated and pressured. Ultimately, hosting is take-it-or-leave-it; it's a gift, and the gift giver has all the power over what the gift will be, even if they do try to please the recipient.):
She is one of your closest friends, I would think you can let her in on the situation a bit and still include her if you want.
You can sort of ask her to meet you halfw ay on the compromising.
"I thought of you. I am serving a large leafy salad and will provide low-cal dressing. The entree is x with y and z for sides. Save your points and let me know if you want a smaller helping of x, y or z. And there will be fruit as an option instead of dessert. I do hope you can save your points and come, and I am trying to arrange it so that it meets your needs without having to cook two complete meals, as that wears me out!"
and then *stop caring* whether she's happy with the menu. Detach yourself. "Oh, well."
And you know what? If you really feel backed into a corner, there is nothing wrong with gently reminding her: "Weight-Losing Friend, I'm not a restaurant. If my company is not important enough to you, for you to make do with the foods that will fit your diet plan, then please don't come to my home."