What communication interfaces do you have on both the modem and the LCD? The 6009 has 12 DIO lines that you could potentially use for this purpose, but note that they're software-timed with no FIFOs. Implementing a UART (assuming you need serial control for the modem) using the 6009 alone probably would not be the best course of action. I don't know what interface you have on your LCD; I've seen both parallel and serial interfaces for LCDs.
Do you expect the 6009 to power both the modem and the LCD, or will they be powered independently? The +5V output on the 6009 is rated to 200mA max, and the +2.5V output is only rated to 1mA.
I think you'd need to describe what you're trying to accomplish and what parts you're using before anyone could give a good recommendation either way.
