It should work with OpenOCD as it supports both FT2232 based JTAG dongles and the STM32F4. I'm not sure if the config in the EEPROM of the device will be supported though.
I am not sure about the ATmega as I have never tried to program those over JTAG but it should be fine as long as either the Atmel tools support the FT2232 or you can make OpenOCD to program the ATmega (you should only have to write a configuration file at most).
You'll have to have a look at the schematic of your Lattice eval kit. My MachXO board has got an FT2232, too (which unfortunately I blew last week
). On that board one of the FT2232's interfaces is connected to the CPLD
AND the JTAG header, so only one interface is easily accessible.
You can always solder some fine wire to the pins of the IC itself, of course.