The Lyra with the ethernet port would require a case mod since it wouldn’t fit in the regular PicoCalc case.
I think the plan to use an ESP32 for wireless is a better idea, and should fit in the existing case:
Personally, I’m hoping to use the USB-host cable for Lyra to connect a USB dongle and add wifi/bluetooth. I don’t think anyone has tried that yet, but I’m hoping drivers exist in Linux for it. (They do in full Linux ports, but I’m not sure what has been removed or changed in the version of Ubuntu that runs on the Lyra.) If that doesn’t work then I’ll try to go the ESP32 “custom dongle” route as well.