Is there a specific time scale in which energy conservation holds true? 
Lenz’s law is a manifestation of the conservation of energy. The induced emf produces a current that opposes the change in flux, because a change in flux means a change in energy. Energy can enter or leave, but not instantaneously. Lenz’s law is a consequence. As the change begins, the law says induction opposes and, thus, slows the change. In fact, if the induced emf were in the same direction as the change in flux, there would be a positive feedback that would give us free energy from no apparent source—conservation of energy would be violated. Source: Lumen Learning

I have a doubt in the bolded part, does this mean there is some sort of transit time for energy? And hence, a minimum time period required for conservation of energy/ first law of thermodynamics to be true?
$$dU=dq-PdV$$
 A: Energy conservation is a law and when writing the exact field equations it should hold at all times t.
Maybe this argument about conservation of momentum can be used:

Momentum must be conserved in the process, so if q1 is pushed in one direction, then q2 ought to be pushed in the other direction by the same force at the same time. However, the situation becomes more complicated when the finite speed of electromagnetic wave propagation is introduced (see retarded potential). This means that for a brief period the total momentum of the two charges is not conserved, implying that the difference should be accounted for by momentum in the fields, as asserted by Richard P. Feynman.

Italics mine.
For that brief period the energy should be conserved by the classical Maxwell consistent electromagnetic fields.
See the details of  the figure in the link on the right.

Lenz's law tells the direction of a current in a conductor loop induced indirectly by the change in magnetic flux through the loop. Scenarios a, b, c, d and e are possible. Scenario f is impossible due to the law of conservation of energy. The charges (electrons) in the conductor are not pushed in motion directly by the change in flux, but by a circular electric field (not pictured) surrounding the total magnetic field of inducing and induced magnetic fields. This total magnetic field induces the electric field.

