Hi, David,
I think you have several options, first of all, you can use the serial interfaces such as SPI, I2S, I think that the SPI bit clock can reach up to 50MHz as master, can reach up to 25MHz as slave. For the I2S, the bit clock can reach up to 6.144MHz.
As an alternative, I suppose that you can use parallel transfer, for example, you can use an external FIFO, on the LPC55XX side, you can use one group GPIO port as data bus, another group GPIO as control signal, you can access data to/from FIFO.
Hope it can help you
BR
XiangJun Rong