Ah, good call, Sundogak... I had made a custom config for Demon Souls at some point and that is the game I have been testing with. So, if I check all the boxes in the custom config it does close the RCPS3 launcher after the game closes. I guess my main wish would be if I could, like a lot of other emulators, launch through LB and completely hide the RCPS3 launcher as well... but thanks for helping me get the launcher to close.
*edit* The LB options you mention might do the trick, but they are LB Pro features and I let my LB paid subscription run out a long time ago, so I can't use those.