The Lennard-Jones force field is a very short range force with a behavior determined by the sizes of the effector and effected particle. At a distance smaller than the combined sizes, the field is very repulsive and after that distance it is attractive. It tries to keep the particles at an equilibrium distance from each other. Particles need to be at a close proximity to each other to be effected by this field at all.
Particles can have for example both a charge and a Lennard-Jones potential, which is probably something for the nuclear physicists among us.