Lenz Law says that the induced current will circulate in a direction such that it produces a magnetic field that is opposite to the change of applied magnetic field. For example, if the loop is a circle on the screen, and the applied magnetic field is increasing and pointing out of the screen, then the induced current will be clockwise. So that the field produced by the induced current is pointing into the screen.
We also know that the magnetic moment due to the current loop follows the right-hand rule. So I think the magnetic moment created by the induced current is point into the screen.
But energy-wise, the interaction energy between the magnetic moment will be
$$U=-\vec\mu \cdot\vec B$$
It means the energy is positive between the moment by induced current and the applied field. So does this mean Lenz Law favors higher energy? Does this make sense? I must have missed some critical parts or misunderstood some critical concepts. Can you help?