0.6 to 0.7 gr is way too much variation ....
but yes, the Dillon powder measures will let you drop consistent volumes of powder / holding 0.1 grain is no big deal on my Dillon 650 ( with a suitable powder - like Hodgdon TiteGroup or Hodgdon Universal ).
Most presses these days are well made ...and I can't say that I've spent a lot of time looking at the Lee Turret press lately ...but my hunch is / you can improve the accuracy on that powder measure by going back / re-running your setup ..and making sure everything is as it should be.
You may have a static issue or any number of things that is causing the problem on a new press ( get some anti-static dryer sheets / clean everything / wipe everything down - see if it helps). Talk to some local guys with the same press / maybe someone can come by and give you a hand with it - and figure it out.