Sounds to me like the dmd is nearly dead, once they warm up they will start working again . Be careful as it will be drawing more current than normal and might damage the high voltage section of the controller , I recommend you try another machines dmd if you have one available to confirm this.

I agree as it sounds like it is dying. Best to test the DMD in another game.

Good news. You can put in a ColorDMD and no longer worry about the high voltage either.
http://shop.colordmd.com/led-replacement-display-for-star-wars-pinball-machine/

Hmmm, I’ve noticed mine do the same thing on occasion. Also with a relatively new xpin power supply. I’ll have to do some investigating (or wait for someone to post the answer here

Any mods in the game? Does you JP or LAH have a Xpin power supply?

From my experience with my LW3 it is normal for the DMD to occasionally not light up immediately on power up. I can't say why but its been like that for over 2 years without any problems whatsoever. The DMD just skips over showing the ROM versions of the CPU and display driver and FREE PLAY or PRESS START is the first thing to be seen. LW3 has the exact same board set as Star Wars. I wouldn't worry about it.

With 3 games having the same game boards, you can easily swap to find out which is causing the issue. Might be easier to swap the whole speaker panel to start with, which will be the DMD and the DMD controller board.