I went through this confusion once so giving you a hint. Take Coul/Debye potential (i am not saying pure Coulomb because u will struck with long range and short range separation there) and give a test run with SI unit say.
I am sure u will resolve the missing 1/4piepsilon mystery
Write the pair potential from Lammps itself. Compare it with you analytic form and you will find your confusion gone (beware that lammps will write pair potential only up to cutoff).