"Close Active Window" is the binding in BB you need to set to exit out of a game back to BB. All the emulators you mentioned should work fine without anything special. At least on my cabinets they do.
How "Close Active Window" works is LB/BB will send common exit commands to the emulator. It will try "Esc", "Alt+F4", "Ctrl+F4", and I believe a few others. Some emulators may be picky and you could use an AHK in the "Running Script" tab of the emulator set-up in LB.
Give this a test: Make sure you have the appropriate buttons mapped for the controller you are going to test with in BB to "Close Active Window" then in LB go to >Tools >Manage >Emulators and edit the emulator. In the "Running Script" tab paste the AHK below and save. Then test the game and see if it makes a difference. This is a simple AHK that has worked for many users. Also make sure the emulator does not have an active setting to "Confirm Exit" or "Confirm on Stop" like some do.
$Esc::
{
WinClose, ahk_exe {{{StartupEXE}}}
}