Lenz's law states - The direction of current induced in a conductor by a changing magnetic field due to Faraday's law of induction will be such that it will create a field that opposes the change that produced it.
The induced EMF produces a current that opposes the change in flux and hence energy. As the change starts, induction opposes and slows the change. If the induced EMF were in the same direction as the change in flux, then that would give us free energy from no apparent source violating conservation of energy. Thus Lenz's law is in accordance with the law of conservation of energy.