Lacewood is awesome. Kaytrim, this will be one hot stick.
Here are my two cents:
Polyurethane (varnish) will bring out the grain just fine.
Do not stain unless you can get an oil based stain.
Before you do anything to seal the wood make sure that all traces of glue are gone from the outside of the box. You can wet the wood with mineral spirits to see if any glue is still on the edges. Mineral spirits will not raise the grain on the wood.
Have fun with your router. 
Thanks for the tips Timoe. I belong to a wood workers forum where I am getting similar tips on how to finish this piece. The box sits only 2" high and I have another board ready for cutting that will only be 1 7/8" high. These will not be for Happ parts they are way too big. These boxes will be setup for Sanwa JLF joysticks. And routers can be real fun or a pain, see next paragraph.
I took my test piece, cut and assembled it just like one of the corners on the real box. I then ran it through the router table. It tried to take the piece out of my hands. My router is a variable speed and I had it set at a medium low speed. I don't know if I should use a higher speed or not. I am afraid that if I do it will throw it across the room. After taking my time and making sure I had a good grip on the little bit of wood I got the routing done last night.
Then I took my orbital sander clamped into my bench vice with 220 grit paper and sanded it smooth. My sander is also variable speed and I had it set on the slowest speed it could produce. This allowed me to have a good measure of control. After sanding I washed off the dust and any glue on the face of the wood. I looked it over and by a stoke of luck I had glued the two pieces with the grain in matching directions. After the router did it's work the corner has grain sweeping up from both faces. I'll have to get a pic posted so you can see how cool it looks. I just hope that I was as lucky with the box. It should still have that detail but the two pieces joining at the corner may sweep in opposet directions or both may sweep down. I'll find out when I take it to the router table tonight.
After discovering that little detail I really want to bring out the detail of the grain now. One thing that I will have to keep in mind, this is a very porous wood. You can even see the pores in places they are so big.
TTFN
Kaytrim