How did Lenz derive his law? I read about it but am not sure if it actually follows from the law of conservation of energy. I tried reading some reference books but could not find the derivation of the law.
 A: You can read the original here. Since this is german and I'm also interested in this question I will try to translate the important points.
In the first paragraph he takes reference to two rules defined by Faraday, namely that

1) a galvanic current induces a current in the opposite direction in an approaching, parallel, wire while the same current generates a current in the same direction when the same wire is receding and that 
  2) a magnet generates a current in a conductor, which is dependent on the direction the conductor crosses the magnetic lines during his movement,

and says that firstly two rules are defined for one phenomenon and that secondly those are not sufficient, since there are cases which cannot included by those rules, and thirdly that they are not simple enough, implying that he is not satisfied with those rules.
In the next paragraph he mentions work of an (apparantly italian) physicist Nobili, whose work builds up on the first rule of Faraday and in which he tries to explain all induced currents in this manner. Again Lenz is not satisfied since this explains not the current induced in a wire perpendicular to a current carrying wire, where the first wire is moving along the second. He also mentions a counter argument of Faraday: when you spin a magnet around his axis and arrange the wires in a suited manner then there's also a current, without wires approaching or receding. 
In the third paragraph he says that after reading Faradays work he's convinced that all experiments regarding the "electrodynamic distribution" (elektrodynamischen Vertheilung) can be traced back to electrodynamic motion and that if you know the latter you know the former.  
Now comes his rule (p.485):

Wenn sich ein metallischer Leiter in der Nähe eines galvanischen Stroms oder Magneten bewegt, so wird in ihm ein galvanischer Strom erregt, der eine solche Richtung hat, daß er in dem ruhenden Drahte eine Bewegung hervorgebracht hätte, die der hier dem Drahte gegebenen gerade entgegengesetzt wäre, vorausgesetzt, daß der Draht nur in Richtung der Bewegung und entgegengesetzt beweglich wäre. 

This can be tranlstated to

If a metallic conductor moves near a galvanic current or magnet, then a galvanic current is induced in the conductor. The direction of this current is such that it would have created a movement in the conductor which is opposed to the movement given to the conductor, under the condition that the wire can only move in the direction of the movement or opposed to it.

Then he simplifies this to this:

If one wants to know the direction of the induced current created by the electrodynamic distributions, one has to think which way the current has to go if one wants to create the movement: the current will be induced in the other direction. 

(I think in the last paragraphs "movement" -- literally Bewegung in the text -- is that what we call now "change in flux".)
In the rest of his paper he gives examples where his rule works. So to summarize: he was not happy with the rules given by Faraday, so he invented a new one. ^^ 
