Okay so I looked and looked and I don't know what I'm missing, but STOWIKI tells me that I can do the Gorn Minefield daily for 1440 chewy chunks of dilithium.
I have seen other people post that they can't get the dilithium and the only response that tried to answer it says that it is a rare mineral pickup or something you have to do during the mission. Seems like that would be in bad form, you know, "Hi guys, let's start killin stuff! Oh you go ahead and dive into combat, I'm going to dig under this tree over here for my loot while you cover my rear... kay?"
At the mission end there are still tons of Gorn about and everyone else ejected back to sector space, so I'm left dodging the Gorn who remain after the wholesale slaughter (it's the new Star Trek way) we just heaped on their race, and trying to look for the loot.
Well since I'm posting this, you can guess that the adverture was fruitless. Can someone clue an old guy in on how I go about ripping off those greedy lizardmen for MY LOOT!!!