Hi. Actually the unit of LJ time is tau_LJ = sqrt(m*sigma^2/epsilon) - do
the dimensional analysis.
As far as the temperature damping time, a typical time is of order 1
tau_LJ. This time should be at least of order 100 timesteps.
For the pressure damping time, there are various ways of selecting it. Do
you want the system to be overdamped or underdamped? You need to think
about what you want it to be in terms of the stress relaxation times of
the system. I tend to set it to of order the fastest stress relaxation
time, which is the time for sound to propagate across the system
diagonally. Also, this time should be large compared to the temperature
damping time. The sound velocity is something like 4 sigma/tau_LJ.