Once the processor is locked, is it possible to debug or flash a new application?

Yes, it is possible to debug or flash a new application into the processor after connecting it through JTAG by providing the 128-bit security key. However, once the processor is locked, only secure applications are allowed.

For more information, please refer to the sections "Programming the Secure Boot Stream into a Storage Device", "Locking the Part" and "Secure Debug Access" in the EE-366 application note linked below:
https://www.analog.com/media/en/technical-documentation/application-notes/ee366v02.pdf