Dimensionalization of LJ units in LAMMPS

I use the Langzhiwan kinetic equation to simulate the aggregation process of nanoparticles.
Here is my script:
units nano
dimension 3
boundary p p p
lattice sc 6.0
atom_style sphere
neighbor 1.0 bin
neigh_modify every 1 delay 0 check yes

region box block -12 12 -12 12 -12 12
create_box 1 box

create_atoms 1 box

set type 1 diameter 3
set type 1 mass 1

pair_style lj/cut 2.5
pair_coeff * * 1.0 1.0 2.5

velocity all create ${T} 12345 dist gaussian

fix 1 all nve
fix 2 all press/berendsen iso 1.0 1.0 100
fix 3 all langevin 300 300 1.0 12345

#timestep 0.00001
thermo 100
thermo_style custom step temp pe ke etotal press
dump myDump all custom 100 dump.nanoparticles id type x y z vx vy vz radius

run 1000

The particle diameter in the script is set to 3nm,
If I want to simulate particles with a diameter of 30nm,
So should the sigma, epsilon, and truncation radius in the potential function change?

If I want to dimensionless the system using LJ units, with a selected feature length of 60nm, feature time of 1fs, and feature mass of 1kg, how should I normalize other physical quantities in the script?

Similar questions have been asked many times on this forum in the past, please take a look. Also, the LAMMPS page about unit system is a good reference for LJ units: units command — LAMMPS documentation

But the Lennard-Jones potential completely ignores that property.
Lennard-Jones applies to point particles.

That question indicates that your knowledge of potentials and forces and particularly the Lennard-Jones potential is insufficient and you need to learn about this.

If you have specific values that you want to simulation, why not use them directly but use a unit system that you don’t understand well enough? You are just making your life needlessly more complicated. If necessary, you can always convert to reduced units after the simulation and only for the properties that matter to you.