The MRI experience was initially optimized for the mbed 1768 device as the primary goal was to provide a production quality debug solution for this specific device. This was before mbed had added the CMSIS-DAP debugging functionality to the device. The project has however been architected so that it already works on other boards featuring a LPC176x processor and is easy to port to other Cortex-M3/M4 based devices. As long as you are using a LPX17xx device which doesn't have a JTAG debugger attached and you can connect the PC to one of the UARTs on the device, MRI should have a good chance of working with it.
Note: When a JTAG debugger is attached to the device, as you have with the LPCXpresso 1769 device, then MRI will hang during startup and debugging will not be possible. This happens because MRI will assume the JTAG debugger is the mbed interface chip and attempt to disable it with special semi-host calls. In these scenarios the user should take advantage of the existing JTAG debugger and skip MRI.
Support for other devices has been added over time. The current list of supported devices can be seen in the following table.