If the IO standard you chose meets the VOH, VOL, VIH and VIL specification of FX2LP then it should work fine. You should be able to look this up in the FPGA datasheet did you check this out?
What is the failure pattern you're seeing when you use the 3.3V IO standards? Does the LVTTL need external pull-up?
Thanks Anand. After checking the FPGA's Voh, Vol, Vih, Vil, it looks that the LVTTL 3.3, LVTTL3.0, LVCMOS3.3, LVCMOS3.0, LV2.5 are all compatible with FX2LP. By reading the Cyclone III's manual again, it looks like the selection of IO standard in Quartus II is actually meant to select the current strength rather than voltage. The IO voltage has already been determined by the hardware anyway. Thus it should not be selectable in the software. Therefore I check the FPGA program again and find the there is one input fed by FX2LP has a more than 400 fan-outs, but FX2LP's Iout is only about 4mA. After reducing the fan-out of that pin, the program seems to be working fine under all IO standard options.