Hypothesizing about the lookup table is an irrelevant question, because no such thing can exist in the real universe. Not even in theory. Moreover, your lookup table contains some amount of information in it; either it was generated by a relatively small polynomial process, in which case for as large as the lookup table appears to be, it actually isn't, and is indistinguishable from simply using the program that was used to generate it, or it does indeed contain exponentially large amounts of information, in which case hypothesizing an exponentially large source of information for the mere purpose of passing a Turing test is a bizarre philosophical step to take. Where is this exponentially large source of information?
Recall that in information theory, being a bit sloppy but essentially accurate with the terms, the amount of information something has can be expressed as the smallest possible encoding of something. The entire Mandelbrot set, as gloriously complicated as it may look, actually contains virtually no information, a mere handful of bits, because it's all the result of a very simple equation. No matter how gloriously complicated your enormous hash table may look, if it was generated with some humanly-feasible program and nigh-infinite amounts of time, the information content of the entire table, no matter how large, is nothing more than the size of the program and perhaps a specification of how long you let it run.
Basically, the whole "big lookup table" has to have some sort of characteristic to it. Either it was created by a program, in which case the program itself could pass the Turing test, or it is somehow irreducible to a program's output, in which case in your zealous effort to swat a fly you vaporized the entire Earth; you can't agree to the possibility a machine might pass the test (or be sentient or whatever) but you can agree to the existence of an exponentially complicated source of information? That's only a gnat's whisker away from asking "Well, what if I use magic to create a philosophical zombie," (I'm referencing the specific concept of a philosophical zombie here, you can look it up if you like) "that looks like it's passing the test but it really isn't, what then?" Well, I don't know, when you're willing to invoke magic in your defense I'll concede I haven't got much of a response, but you probably shouldn't call that a victory.
The lookup table argument only makes sense nonconstructively, if you merely assert its existence but then don't allow anyone to ask any question about where it came from, or what properties it has.