Interesting, nostalgic and very nerdy 
So, you want to call to a number where your modem is waiting and your question is, can L5 make an audio analog data connection to it? (for a moment there I was confused and though you wanted to connect the modem to L5 to act as a modem for it - from possibly flakey 4G to more robust 56.6 
) Have you done anything like this on linux before?
I think what you need is something like GitHub - kamalmostafa/minimodem: general-purpose software audio FSK modem (search linux audio modem for something that you can install or build to L5) and use that from command line and probably need to call manually with AT commands from command prompt to get L5 audio softmodem to a phone connection (that can maybe be set up as a script under a gui icon). This is just a guess.