The EEPROM allows a user to overwrite the FX2/FX2LP default Cypress VID/PID/DID with a user's unique VID/PID/DID information. It is fine not to have an EEPROM during the development phase and use the cypress default VID/PID for the development phase. But for the final product user must use their OWN VID/PID/DID. This is a requirement for getting the device USB certified. In order to overwrite the default cypress VID/PID/DID with the vendor VID/PID/DID an EEPROM is required to be on the I2C bus.
If you would like to eliminate the need for the EEPROM but yet have the Cypress default VID/PID/DID information overwritten by the vendors VID/PID/DID information, you may do so with an external processor wired to the FX2. Basically have firmware running on the external CPU that behaves like an I2C slave device: EEPROM. The FX2/FX2LP on power-up will probe the I2C bus for the presence of an EEPROM and the external processor wired to the I2C bus must respond like a slave EEPROM device providing the VID/PID/DID information..
This method is targeted for FX2/FX2LP designs that ALREADY have an external CPU/processor wired to the FX2/FX2LP that can provide the VID/PID/DID information via the I2C bus on power-up.