In the documentation it says lj timestep is t* = t x tau
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No, the length of the timestep is set by the "timestep" command, not the "units" command.
The documentation of the "units" command says that the *time*--not the timestep per se--is tau, and tau = t * norm_fac, where norm_fac is a normalization factor, and t is an unnormalized time. t* is an alias for tau. The units of t depend on the units of norm_fac. For example, if norm_fac is in units of 1/second, then t is in seconds.
The LAMMPS documentation has norm_fac = (Kb T / m / sigma^2)^1/2, but I think that it is supposed to be (epsilon / m / sigma^2)^1/2.