The FX2LP is the generic USB controller having lot of flexibility compared to its fixed function counterpart SX2. The FX2LP is a full fledged USB microcontroller. It is basically an enhanced 8051 with an integrated SIE. It has 16K of internal RAM for code/data load.
The EZ-USB SX2 as you know is an SIE only device. It does not have any RAM for code download. It needs an external master to initialize its registers and have the device enumerate. The SX2 can also function as a standalone device. The SX2 responds to standard USB porotocols. It does although need the VID/PID from an external EEPROM or the external master.
If there is an external master processor selected and the 8051 capability is not needed, the FX2LP needs to be used in the Slave FIFO mode. In order to have the FX2LP behave the same as the SX2, a firmware loaded has the loaded in to the internal memory that interfaces with the external master which is there.
From a programming viewpoint, there is no command interface in the FX2LP that will allow the external master to interface with the FX2LP to access registers. The FX2LP has two Address pins (as opposed to 3 in the SX2). The 8051 can access any registers at any time and output this value to the external master via GPIO port pins or the Slave FIFO interface.