Why is an elliptical wing planform so aerodynamically efficient in layman's terms? Below is part of an answer to the post 'For the elliptical wing, what is elliptical, and why is drag regularly distributed?':


  On the untwisted elliptical wing the local lift coefficient is constant over span, and changes in angle of attack over the linear range will change the lift coefficient equally everywhere. This, when combined with the elliptical chord distribution over span, means that the circulation distribution will stay elliptical over the linear angle of attack range. This is the special characteristic of an elliptical wing: While any wing can have an elliptical circulation distribution at one angle of attack (given the right twist distribution), the elliptical wing will keep that elliptical circulation distribution over the whole operating range.


My question is: how can the wing tips of an elliptical wing be considered to produce the same amount of lift as the root (see emphasis above)?
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.