Is the Lennard-Jones potential applicable to any phase of a substance?

The Lennard-Jones potential describes long-range attraction and short-range repulsion. In both solids, liquids, and gases there are attractions and repulsions.

1. Does it mean that Lennard-Jones form of potential is applicable to any phase of a substance?

2. If yes, does the attractive and repulsive parts of the potential have the same origin in all phases?

Let's start by saying that the LJ potential is a very, very crude approximation to a real atomic potential: the $r^{-6}$ term can have some sort of justification because we can say that it comes from dipole-dipole interactions, but the exponent $12$ of the repulsive term is completely made up and has no theoretical justification whatsoever.