In simple terms magnetic levitation occurs when two opposing magnetic fields are present. This results in a magnetic force pushing an object up. If the magnetic force is equal to the gravitational force, the object will levitate.
In superconductors, a superconductor actively excludes a magnetic field from penetrating it. The produces a second magnetic field causing the levitation. It isn't an example of Eddy currents and lenz's law. It is called The Meissner Effect