Hi,
I have not good idea to invert a signal from a pad and output an inverted signal to another pad without interrupt for LPC824.
But the LPC804 has PLU, which enable you invert a signal from the PLU input pad and output the inverted signal to another PLU output pad.
This is LPC804 website:
https://www.nxp.com/products/processors-and-microcontrollers/arm-microcontrollers/general-purpose-mc...
Of course, you can use PINT module to generate interrupt, in the ISR, read the logic of input pin, and output the inverted logic to another GPIO pad.
Hope it can help you
BR
XiangJun Rong