Contrary to what the astronomers and geophysicists would tell you, it would seem that mineralogists have a sense of humour. Dilithium, the fictional mineral from Star Trek can be found in this otherwise serious database here: http://webmineral.com/data/Dilithium.shtml
Dilithium does exist in the form of dual bonded Lithium atoms (Li2). However the entry in this database refers to the fictional crystal, a "bottle brown," non radioactive substance that focuses the matter/antimatter streams on Federation Starships. The crystal structure is composed of Tellurium, and Lithium (Li2Te), which is "confirmed" by the following citation:
Nemoy, L S; Doohan, J, Star Fleet Transactions , 1 (2364) p.239-444, First Star Fleet Federation Symposia on Deep Space Findings from the, Enterprise NCC1701A VoyagesWhat an age to live in.