I've not used the PCF8574, but I have done it with a 74HCT595 on several different LPC devices (needs 6 pins in total). The 74HCT595 is quite a bit cheaper than a PCF8574! Connect the HCT595 outputs to D0-D7 on the display and write to it using the SPI port (it just needs SCK and MOSI)
Then use four other GPIO lines to do RW, R0 and E connecting RW to the OE pin of the 74HCT595, and E to STCP. Set RW and R0 before writing the data to the HCT595 then pulse E when the SPI write is completed.
This implements an 8-bit output-only port, but you also need to read back the busy pin, but you only need read D7, so connect that to the fourth GPIO line.
Trap for the unwary: LCDs and OLEDs like a 5V supply, and don't like the logic levels from a 3.3V processor. Hence using an HCT595 on a 5V supplies, the HCT (rather than the HC) accepts 3.3V logic levels happily.
R0, RW and E will also need a 3.3V to 5V level shifter (two sections of a 74HCT04 per pin)