1. Share your 25AA02UID schematic, I need to check whether your external EEPROM circuit have problems or not.
Pin 3 (Write-Protect) and Pin 7 (Hold) are active low. These are pulled up to Vcc (Pin 8).

2. Share the photo about the connection between the external EEPROM and your LPCXpress 54114 board


In the left figure, as the board is *upside down*, Pin 1 is in the upper right. Can see Pins 7 and 3 connected to Pin 8 (Vcc=Vdd)
In the right figure all connections are to the upper row of the J4 PMOD connector *EXCEPT* 'Chip Select' which goes to J4, pin 7. NOTE that *unlike* DIP package, Pmod pin numbers go top-to-bottom (i.e., holding the board vertically) *on both columns*. Column 1 are pins 1-6, Column 2 are pins 7-12.
3. The 25AA02UID VDD and VSS should powered by the LPCXpresso54114 board, it is 3.3V supply.
They are: Vdd - J4, Pin 6 and Vss - J4, Pin 5 on Pmod connector
4. Provide your whole test project about the EEPROM, you can deleted all the other functions, just give me the simple project which can reproduce the problem.
OK. I do not see the 'Advanced' icon. If I do not see it when I 'Post', I will attach to a separate mail.
Please also tell me what the IDE you are using.
Using MCUXpresso V10.3.0
5. Tell me the SPI pin you are using in the LPCXpressso54114, eg SPI_CS is J1_XX, then I will help you to test it, it will save both you and my time.
SIGNAL LPCXpresso Pin# 25AA02UID Pin #
SPI_CS J4, Pin 7 Pin 1
SPI_CLK J4, Pin 4 Pin 6
SPI_MOSI J4, Pin 2 Pin 5 (SI)
SPI_MISO J4, Pin 3 Pin 2 (SO)
Vdd (+3.3) J4, Pin 6 Pin 8
Vss (GND) J4, Pin 5 Pin 4