Lenz' s law for electromagnetic induction :
emf = - dФ / dt , Ф = Sum Integral B * A
When a permanent magnet SN creating a magnetic field B is moved in and out of a simple circular loop, the magnetic flux Ф through the loop changes in time. The external agent puts in work on the permanent magnet to make it move.
The induced emf is such that it produces current in the loop in a suitable direction. The current induced will result in a magnetic field B2 and flux Ф2 which counters the dФ ie., if dФ is positive, then B2 & Ф2 will be in opposite direction to Ф. So the change in Ф is opposed. So the induced current in a loop will try to restore Ф back to its previous value. Thus the induced current resists the either movement of the magnet towards and away from it. So the external agent has to do work to move the magnet and cause changes in flux.
The work done by the permanent magnet movement is converted in to electrical energy in the current loop in the form of emf. The power / energy is dissipated in the resistance in the loop as heat. So in this case the energy is conserved and converted from mechanical form to electromagnetic and then in to electrical energy and then finally heat/radiation.
In case Ф2 will act in the same direction as dФ, then the change will recursively increase Ф. The magnet will get pulled in to the circular loop without any work from the external agent. The energy stored in the form of magnetic flux in the loop will increase continuously without any input energy from any where. The magnetic will accelerate indefinitely. Since this not possible.
Hence, Lenz's law with emf induced opposing change in flux, is the right choice. So the minus sign in front of dФ/dt. Further, it can also be proved that the power dissipated in the loop is equal to the work done by external agent in moving permanent magnet.