FX2LP is a high speed capable device. Although the theoritical bandwidth is 480 Mbps~60MBps, but the actual data rate will not be so much. You can check this by using Cypress streamer application in bulkloop mode. You will need to stream both the endpoints in 2 streamer if the firmware is bulkloop.
You do not necessarily need any external memory. You can use the device in no EEPROM mode. You can write the host application to program the firmware on the FX2LP and stream the data. You can take help from the Cypress Control center and Streamer host application source