I don't have/use a LPC4370, so I cannottest code myself.
But first, it should be clear that you cannot output 120MBps ADC data over a 0,0096Mbps UART channel in realtime. I am pretty sure the LPC4370 has no output channel which can sustain this high data rate in a feed-though manner, you will need to buffer the ADC data in RAM.
Secondly, with a 80Msps rate, internal bus bandwidth can become a problem, and needs at least a consideration. I am quite sure an interrupt-based approach will not work out, you will get ADC overflows immediately. You will need to setup a DMA channel for the number of samples your ADC is supposed to take. I would check the LPC-Link sources, how they do it. Perhaps even use this project as starting point for your project.
> BTW, I did try to set the baud rate to 9600 but with no luck. ...
The simplest way would be to enable semihosting in the project, and add PRINTF calls in the debug version of your code/project. These outputs are routed via the debug adapter, and it's VCOM functionality, and show up in the debug console of the IDE. If you want to a separate UART, you could use a UART example from the LPC4370 SDK, and adapt it if necessary.
As stated before, do not try outputs/printf, or other calls during the sampling phase, this will not work. Run your ADC sampling first, and output via UART/semihosting afterwards.
> Can the RAM store the 80M ADC result correctly? ... What's the maximum speed can ADC run and store into RAM?
Sure. But you will need DMA, which transfers the ADC results directly to RAM.