Everything can be represented as a lookup table. Well, at least everything we can rigorously reason about. Because set theory can serve as a foundation of mathematics. And relations there are sets of pairs (essentially lookup tables).

I guess it means that we can throw away the notion that "it can be represented as a lookup table" has some profound meaning. Without further clarifications, at least. Finite/infinite lookup table, can/can't be constructed in time polynomial in the number of entries. Things like that.