There are 2 points relating to this issue:
1 - For MultiCore debug of the LPC4370 we have observed that the automatic selection of M0 devices may not be made correctly.
The LPC4370 MCU includes a M4 and two M0 (M0Sup and M0App) cores. The M0 devices appear in the scan chain as device 1 and device 2 - where device 1 corresponds to the M0Sub and device 2 as M0App. When automatic device selection is enabled (the default) then LPCXpresso IDE (version 8.2.2) will automatically select the M0Sub core before the M0App core. This may not be the desired connection order!
To override this automatic selection, go to: 'LPCXPresso IDE Preferences -> LPCXpresso -> Debug Options (Misc) -> Disable Auto-select devices on multicore targets' and untick this option.
Before performing a new debug session, you will have to ensure that any incorrect project .jtag files are deleted - the simplest way to do this is to delete the build configuration directory within a project (Usually called Debug or Release).
The potential for automatic selection of the wrong core will be addressed in a future tools release.
2 - When a core connection is made, subsequent selections will only present available devices. For an LPC4370 you would initially expect to see 3 possible devices to debug. If this is not the case then it is likely that a target connection exists to the 'missing' device.
First ensure that the IDE does have a target connection (click the double red square to kill the debugger connection to a multi core target).
If this is not the case then launch the Mac Activity Monitor and type 'red' into the search box. Look for the process 'redlinkserv' and kill this (when running under Windows, the same operation can be performed with the Task Manager).
You should now see the 3 devices available for debug connection.
Yours,
LPCXpresso Support