Advantage of MTZ problem formulation of TSP
The MTZ is not an algorithm.   Miller-Tucker-Zemlin formulation is a method of formulating the Travelling Salesman Problem as an instance of integer linear programming.  This lets you feed the resulting integer linear programming instance into an off-the-shelf solver for integer linear programming, and let the solver solve it for you.

Remember that an instance of integer linear programming is a set of variables and linear inequalities.  Lookup tables are not allowed; the inequalities have to be linear (e.g., $5x_1 + x_2 \le 7$, but not $T[x_1] \le 5$).  Therefore, using lookup tables are simply not an option, if you want to use integer linear programming.

Alternatively, you could skip using an integer linear programming solver at all, and try to solve the Travelling Salesman Problem from scratch.  But good luck with that.  It's an NP-complete problem, so it is unlikely you'll be able to find an efficient algorithm to solve the problem.  (And just saying "use lookup tables" is not an algorithm.)

Bottom line: I think you have a confusion about how integer linear programming works, and what MTZ is.  MTZ is not an algorithm for the TSP.  Rather, MTZ is a way of describing the TSP in a format that you can give to an integer linear programming solver.  Lookup tables aren't an option, if you're using an integer linear programming solver.