Breaking it down we can say:
[I] <need> {to eat} [lunch] [tomorrow]
First question:
Who is "I"?
Is "I" the actor?
Well. The actor isn't eating lunch, are they? The actor is informing you about _someone_ eating lunch, but the actor isn't me.
This seems trivial, but it really, really isn't and the deeper you go down this rabbit hole the more complicated it gets.
I [as in this physical body]…
I [as in this internal psychic vampire]…
I [as in this personality]…
2/