Are There Limitations to Lenz's Law in Real-World Applications?

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Mattara
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What are the limitations of Lenz law? If there where none, you could just move a magnet through a coil and keep moving it away, thus creating the worlds most powerful magnet. This seems highly unlikely.

When moving a magnet towards the coil, the external magnet field induces a current in the coil, creating its own internal magnet field with the same magnetude but with the opposite direction, thus negating the change.

When the magnet moves through and out on the other side of the coil, the current changes direction (?) and the internal magnetfield is increased in the same direction as the outer magnet field is, thus negating the change again.

Does the internal magnet field increase until the magnet is too far away from the coil to be able to generate the current and as a result, the internal magnetfield?
 
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The limitations of Lenz's law are that it only applies to situations where there is a change in the magnetic field - it does not create a permanent magnet field or continue to generate a current once the magnet has passed through the coil. This means that the internal magnet field created by the current will eventually dissipate away and there will be no further effect on the magnet. This means that it is not possible to create a permanent magnet field or keep moving a magnet away from the coil and creating an ever-increasing magnetic field.