No, you don't need to find Dilithium. Trouble does go looking for Lithium Rain though, most illogical
For this you will need to create the dual laser module with white LED saucer lights.
I salvaged the parts from two small laser pointers that I found at the dollar store. They are a combination LED flashlight and red laser pointer.
For the shirt, I found a shirt at the outlet mall that was pretrimmed with black in the neck and sleeves. It fit the look of The Original Series Star Trek uniform. You can always add the collar trim and sleeve braid to a solid color shirt of your choosing.
You will need an inkjet printer to print out the ship and the starfleet crew badge. Print out on dark iron on transfer paper and iron it on to the shirt.
You will need a piece of iron on fusible interfacing to reinforce the area where the laser module is attached to the shirt.
Other materials and skills needed are the tools to do soldering and some essential tools for electronics work.