How to convert real units to lj

Dear everyone:
I’ve read manual and achieves in maillist but i still confused about how to convert unit.
The why i should do this is that i need to compare my data to someone who have published.
First, if there is two types of particle:

units real
pair_style lj/cut 10.5
pair_coeff 1 1 0.112 4.01 10.5
pair_coeff 2 2 0.224 8.02 21

can i to do convertion like this:

units lj
pair_style lj/cut 2.61
pair_coeff 1 1 1 1 2.61
pair_coeff 2 2 2 2 5.23
That means i implicitly let epsilon=0.112, sigma=4.01. But in manual i read this "LAMMPS sets the
fundamental quantities mass, sigma, epsilon, and the Boltzmann constant = 1 ". Is that means LAMMPS already have a fundamental value to do this?

Second is about to reduced unit of time.
tau = sqrt(epsilon/m/sigma^2) * t
if i want to get a proportional value to real units, does i need to firstly convert femtosecond to SI of second ,
then multiple sqrt(epsilon/m/sigma^2)?

Im sorry to ask this too elementary question but i really confuesd.
Thanks !