I just found a fix for Android and Sharp x68000. Just navigate to the "LaunchBox/Data/Platforms" directory on your phone using a text editor like "QuickEdit" (free downloaded from GOOGLE play store)
Open the file "Sharp X68000.xml"
Change line 5: <DefaultEmulator>Custom Emulator</DefaultEmulator> to <DefaultEmulator>RetroArch</DefaultEmulator>
Insert line 6: <DefaultEmulatorCore>px68k_libreto_android.so</DefaultEmulatorCore>
Save the changes + restart LaunchBox and you are all set.
Broken on Android for me as well. It detects it as "Custom Emulator" and I haven't seen a way to change it.
On Windows it is missing the Emulator config for Sharp x68000.. I added entry, linked it to RetroArch and and it works fin now on Windows.