Nobody claimed that there is an algorithm to translate arbitrary programs into an equivalent lookup table. (Because that's the exact same proposition as stating that there is a program that can compute whether an arbitrary program halts when executed).
The point is: Any specific program can be translated into a lookup table. Computer programs and lookup tables are equivalent!
You claimed that computer programs are somehow "more powerful" than lookup tables. That's just plain wrong. They're exactly equivalent in "power".
Nobody claimed that there is an algorithm to translate arbitrary programs into an equivalent lookup table. (Because that's the exact same proposition as stating that there is a program that can compute whether an arbitrary program halts when executed).
The point is: Any specific program can be translated into a lookup table. Computer programs and lookup tables are equivalent!
You claimed that computer programs are somehow "more powerful" than lookup tables. That's just plain wrong. They're exactly equivalent in "power".