I don't know. Here is how you find out.
Make a list of each pin each unit uses. Are there any the same? If not then yes.
If yes then see if any of the common pins can be reassigned or is it asking too many pins of the same type, like both want to use the serial port. If they can be wire them to these different pins and rewrite the code.
the 2.4" TFT LCD Screen Module: ITDB02-2.4 is just back to a reply on this forum.
"Arduino communicates with both the W5100 and SD card using the SPI bus (through the ICSP header). This is on digital pins 11, 12, and 13 on the Duemilanove and pins 50, 51, and 52 on the Mega. On both boards, pin 10 is used to select the W5100 and pin 4 for the SD card. These pins cannot be used for general i/o. On the Mega, the hardware SS pin, 53, is not used to select either the W5100 or the SD card, but it must be kept as an output or the SPI interface won't work"
so the ethernet module uses, but not physically cuz the ethernet shield is smaller than the arduino but i read the new one is fully complatible
D50(PB3)
D51(PB2)
D52(PB1)
D53(PB0)
now if you compare the lcd uses this pins for SD and i dont think im gonna us SD