People have asked about plotting/exporting the EAM functions before.
Being on-the-fly calculations, one should be able to export the pair part, embedded part, and electron density for each thermo. Can you please tell us how one can see these global/per-atom outcomes?
You can only access per-atom properties that are stored in (persistent) per-atom arrays arrays during the force computation. For the EAM pair styles, these are the local electron density contributed from the neighboring atoms (rho) and the derivative of the embedding energy (fp) as explained in its documentation.
You can access these properties using the fix pair command — LAMMPS documentation