Okay, I talked to Lingo again. No new information, though. The techie just reiterated (in more detail) what they said before: you have to use a fax machine (not a PC) with a 14400 modem, and they don't support T.38.
I asked about fax relay and fax passthru, and was told that they can do either. I asked if I need to do anything to tell the fax machine which protocol to use, and the techie said no.
I'll have to see if I can borrow a machine.