When we move a magnet towards a coil, current is induced in it. Magnetic field too develops around it. Since there is interaction of both magnetic fields(that of magnet and coil), there is magnetic potential energy in field(gained from the work we do). This energy is going to do work on magnet (either in repulsion or attraction). In this case Lenz's law tells us that it will be repulsive force.
If it is attractive or repulsive , the stored energy is to be spent on magnet and it does work on magnet. Also whole of energy we supplied is not used in this work as there is heat loss too. Then why we say it (in case of attractive force by coil on magnet) breaks conservation of energy?