Please read the doc page for the lattice command. Then try it
out for a small system, visualize the results, and write the atom
coords to a file to see if they are what you expect. If you know
what the coords for a 310 surf should be, you can easily verify
that LAMMPS is producing what you expect.
...and don't forget to check, if the simulation cell is a commensurate
multiple of the rotated unit cell, so that you get a proper
continuation across periodic boundaries. most problems that are
reported for non-trivial orientations, are due to this kind of
oversight.