Jonathan Zimmerman forward your email to me as I am not in lammps-users list. I am trying to answer your questions as best as I can. First, I do not have lammps input files as this work was done many years ago when we were still in an old age of paradyn. Essentially I calculated unrelaxed lattice constants with Mathematica, and another staff calculated relaxed elastic constants with paradyn. In the cases where there is no internal relaxation (e.g., fcc Pd), the two calculations match. For your applications, Aidan Thompson has written an lammps input file for calculating elastic constants, which you should be able to find in lammps package. In terms of hydrogen diffusion, my finding was that it appeared to be barrierless. My explanation is that if hydrogen and metal have approximately the same kinetic energies, then hydrogen moves much faster. It does not really lose too much energy to the surrounding metal atoms when jumping. This means that once it can jump, it will remain that ability of jumping for quite a while. These are based on my memory so that you may explore this yourself further, e.g., you may reduce your time step size etc.
By the way, I assume that you are using NVE to simulate H diffusion, right?