That is just a nomenclature issue. A Lennard-Jones potential where the repulsive term has a smaller power than the attractive term makes no sense. If you look at the sign in formula 20, you can see that the terms are swapped around. A more serious issue is the factor of 2 for the attractive term. This means, that this paper uses a different convention for sigma than what LAMMPS uses. LAMMPS expects sigma to be the distance where the potential energy is zero. When the r^6 term has a prefactor of 2, then this means it assumes sigma to be the minimum of the potential, i.e. the sigma values are too large for use in LAMMPS by a factor of 2^{\frac{1}{6}}. This could be a contributing factor to getting too large a distance.
You are using a “generic” force field. The more generic a force field is, the less accurate it is. This may give OK bonds, but I doubt it will be good for the interlayer distances.
I suggest you have a look at the INTERLAYER package in LAMMPS and check out the various provided styles and their corresponding publications for accurate representation of layered materials.
If you prefer a “generic” force field, I would look at Amber (or perhaps CHARMM) and use the parameters for benzene carbon atoms. Those are likely much more accurate since they are parameterized not for a generic carbon atom, but specifically for carbon in an aromatic 6-ring.