So you buy two components from an LGS, and they tell you the problem with their products that should work with each other...but don't...is going to cost you money? I'd find another LGS when this is resolved. And the $45 seems an odd service price for a problem that is most likely the cheaper of the two components...the extension. A gunsmith is necessary for this diagnosis? Seems like needing a full fledged physician to diagnose a mild sunburn. Unless there's more to this story, this sounds like a fairly incompetent LGS. Surely this shop has another Anderson lower and another extension tube to make a quick comparison to see which component might be defective or out of spec. Of course, it's possible the poster could have misthreaded or boogered up the threads in one or both of the components, but that too should be easily diagnosed by the counter man without needing a PHD gunsmith.
On the lubing issue, I always use a small amount of antiseize on the extension. Working in automotive, motorcycle, and even bicycle environments, a little antiseize on aluminum and many steel fastener threads has saved a lot of heartache and gnashing of teeth.