What is the minimum computational temperature in LAMMPS?

We know that T=0K is not allowed for calculating the Nose-Hoover thermostat. Explicitly (fix nvt command — LAMMPS documentation):
" For the temp keyword, the final Tstop cannot be 0.0 since it would make the external T = 0.0 at some timestep during the simulation which is not allowed in the Nose/Hoover formulation."

Then, what is the lowest temperature we can perform simulations with LAMMPS using the Nose/Hoover formulation?

That depends a bit on multiple factors including your choice of units and size of time step. You need a small number that is large enough so you can still get a stable time integration of the fictitious degrees of freedom for the thermostat coupling. Try 1.0e-10 or even 1.0e-100.