The terms “set lunch” or “set menu” - meaning a prix fixe menu or table d’hôte - refer to the fact that the menu and the price are “set,” not to the fact that there is a “set” of items. Just as you wouldn’t say that such-and-such an item is “part of the fixe,” don’t say it’s “part of the set.”
I don’t know how this misuse has crept into usage, although it may have been via non-English speakers.
Obviously what you describe is another meaning of “set.” That’s exactly what I said. But that meaning is incorrect when used in the case of a “set meal.”
This would be a similar example: “Fixed” can mean " attached or set in one place and doesn’t move" as well as “repaired” or “corrected.” A “fixed price” menu doesn’t mean a menu where the price has been corrected, even though that’s one meaning of “fixed.” It means a menu where the price is set and doesn’t change.