Why is an elliptical wing planform so aerodynamically efficient in layman's terms?
I believe that you misunderstood the answer that was posted.  The local lift coefficient is different from total lift.  In fact the question itself states the lift and drag decrease from root to tip.  If you include the previous two lines by Peter you will get a better context:


  It is both the planform and the circulation distribution. Note that circulation is not lift coefficient but bound vortex intensity. You can interpret it as local lift coefficient times local chord.


The amount of circulation created is related to the total lift.  See the Kutta-Joukowski theorem.  Peter says the circulation distribution is elliptical along the span (decreasing towards the tip) so the lift is not constant along the span of the wing.

A more Layman's way of understanding this: The lift decreases at the tip since the chord length decreases but the local lift coefficient remains the same.  Since the local lift coefficient is related to the local drag coefficient this also means that the local drag coefficient remains the same along the span.  But again because the chord length decreases along the span the total drag actually reduces at the tip of the wing.