Dear Steve,
First, thank you very much for your reply!
Second,
When 2 atoms are bonded the weighting coeff
is 0.0, you are turning off the vdwl and Coulomb
interaction between those 2 atoms, hence the
energy will change.
You are ABSOLUTELY right!
Moreover, this is just the thing I wrote in my first post.
When we turn off vdwl and Coulomb interaction between those 2 atoms
the total vdwl and Coulomb energies of the system should alter by vdwl
and Coulomb interaction between those 2 atoms.
Vdwl and Coulomb interaction between those 2 atoms are very easy to
calculate. I did this in my first post.
(There vdwl interaction between those two atoms was zero since the
distance between them was purposely chosen equal to sigma of Lennard
Jones law (viz. 4 A) and Coulomb interaction was, of course, nonzero
and equal to 83.015927)
And it was obvious that the total vdwl and Coulomb energies alter not by
these calculated values but by some absolutely unexplainable values.
Namely, the difference in total vdwl energies was 5.19017 kcal/mol;
the difference in total Coulomb energies was 1858.34 kcal/mol.
I tried four solvers, viz.:

kspace_style none
pair_style lj/cut/coul/cut 12.0 
kspace_style ewald
pair_style lj/cut/coul/long 12.0 
kspace_style pppm
pair_style lj/cut/coul/long 12.0 
kspace_style ewald/n
pair_style lj/coul long long 12.0
In all four cases the differences were the same.
Once more the conditions:
two atoms of one type;
charges are +1 and 1;
LJ coeffs: epsilon = 1 kcal/mol sigma = 4 A;
distance between them is 4 A.
What are interactions between them?
I claim that E_vdwl = 0 kcal/mol, E_coul = 83.015927 kcal/mol;
LAMMPS claims that E_vdwl = 5.19017 kcal/mol, E_coul = 1858.34 kcal/mol.
Who is right?
Best regards,
Vadim