Hi
the LPC55xx/LPC55Sxx provides a simple hardware means called Inter-CPU Mailbox mechanism for communication. On the software, many methods can help to implement communications with both cores. The software methods could be simple or complex. The shared memory is the common base in the methods. Here, the hardware Inter-CPU Mailbox communication mechanism will be introduced.
For detail, I recommend you refer AN12335 LPC55xx/LPC55Sxx Dual Core Communication, Chapter 2.3.
it's simple and readable.
You can also refer "mailbox" demo inside MCUXpresso SDK package.
Have a nice day,
Jun Zhang