@SEEK well im not sure what you mean by "it works the same way.. Le Chatelier's law is a very generalized law, lenz law is a much more specific law that, by virtue of being true, ensures that Le Chatelier's law is not violated.

Think of it in terms of forces, in any system if forces arent balanced then the system will change (usually this means parts of the system start to move).. one of two things happen, in any ideal system things will oscillate forever, this is one form of equilibrium.. in a non ideal system losses due to ineffiency mean eventually the system will come to rest and all the forces in the system will have equal and opposite forces.. The later non-ideal system is what we talk about the vast majority of the time.

In that sense when a change magnetic field is induced on an inductor there will be a force applied to the electrons in the wire, at first there is no equilibrium and the electrons will start accelerating, creating its own magnetic field that is opposite of that of the induced magnetic field. At that point the forces will cancel out and the electrons will stop accelerating and be at a constant speed.

In practice this only works when you consider both inductors as superconductors otherwise the energy will be lost on the secondary side if the primary field is no longer changing.

consider a superconducting coil that is charged and shorted out with a super conducting wire... you have another superconducting coil and wire somewhere else that was not charged. what I described is what would happen when you bring the two loops near eachother and kept them there. The charged coil would act similar to magnet and when it is brought close to the other coil the other coil would induce a current and would act like a magnet as well but of opposite orientation. and with a flow of current that is opposite.