how can lenz law xplain law of conservation of energy??

Lenz''s Law states that the Nature of induced emf in the coil is such that it opposes the causes of it.

It can be explained by a simple understanding of Faraday EM induction experiment. When we push the N-pole of magnet towards the coil, the flux change with coil is such that it develops a North Pole on it. Hence they form like pairs of magnet, which opposes the relative motion. Hence An External force is required to push the magnet. When we pull the magnet out, Coil develops a South Pole which attracts it. Hence Again Some Mechanical Force is required.

Hence Lenz modified Faradays Equation as 

E=-d?/dt

where E=induced emf, ?=magnetic flux associated with it

Negative Sign indicates that the Emf is of opposite polarity than the Magnetic Flux