So, while they are capable of manufacturing diamonds, rubies, emeralds, sapphires--all the crystalline forms that are cherished above all things, evidently (and perplexingly) dilithium is something that can't be manufactured shipboard.
We can manufacture synthetic diamonds today, so it no big surpries that the machinery aboard the Enteprise can do the same. They're spectroscopically different than diamonds that come out of the ground (light passes through them differently), and there is debate as too whether they are real.
I'm not sure where I got this, but supposedly dilithium is chemically the same as quartz and if you attempt to fabricate (or replicate) a synthetic dilithium crystal, all you'll get is a piece of quartz. Likely non-canon.
Does this mean that there still is value in "genuine" gemstones? Well, Kirk certainly seems to think so, when discovering the diamonds in "Arena"!
The diamonds and other gems that Korob creates with a wave of his wand, and the ones manufactured aboard the Enterprise are "meaningless." Yet the diamonds Kirk discovers on the Arena planets are; An incredible fortune in stones.. Natural are valuable, and manufactured are not. ...