I'm confused as a pig in a shirt. Which way is the scope out of adjustment, W or E?
How does lapping the rings help center the scope closer to its' mechanical center? Are we talking about the same thing? Lapping rings (to me) means 'polishing' the inside surfaces of the rings so that they are dead plumb lined up with each other; that way, the rings won't mar the scope tube because of a misalignment of either ring. If the scope base's screw holes are not drilled and tapped "perfectly" in line with the rifle bore, lapping won't help change the relationship between scope and boreline worthy of note (that is to say, if the scope base is mounted out of line with the barrel, lapping the rings will not help 'boresight' the scope any closer to the bore's POA).
What do ya'll mean when you say, "turn" the front ring? Do you mean cant (twist) it so it's direction bears left or right from its' current setting? That won't help at all; it'll be out of line (literally) with the rear ring. No twisting manipulation of either ring singly will solve the scope's lack of adjustment. If there's a windage adjustment on the rings, you might save the situation, or set of Burris Signature Zee rings with the polymer inserts might allow you to adjust for badly drilled scope mount holes.
Are you sure the shop mechanically zeroed the scope reticles? A lot of the time, shops just install scopes without setting the reticles to their mechanical zero. If you're running out of Elevation adjustment, that's a whole different matter; you can use a canted scope base in that case.