Sorry. I'm an idiot. No, "lspci" wouldn't show the modem. I missed that critical
word "external".
If the modem supports the standard "AT" command set, you shouldn't need a special driver. Everything you need should be already there.
Serial-port modems don't actually need modem drivers, since the application program issues the modem control commands and the serial port driver transmits both commands and data without distinguishing between the 2. If you're using the modem to do fax - say if you want to send stuff to Barney the Dinosaur - the Linux fax software handles the sordid details of issuing the fax commands and encoding text into raw image bits.
You may have to set some options based on the brand of modem you have, since the finer details of the command set may vary, but it doesn't require a special driver.