Correct me if I'm wrong but don't you just need the chip that is in the Lightning to USB adapter Mojo people use... I was under the impression that was just for
MFi authentication, not anything related to the digital audio path.
I don't have a Mojo or I'd try it.
The Classic has it's own MFi chip inside the unit. That chip needs to do the handshake, the Classic is not Lightning compatible.
The DAC end (in this case a Mojo) also needs to have the authentication chip (i.e."Made For iPod"), but the Mojo lacks that feature in terms of iPod Classic compatibility and only offers standard USB OTG connectivity using either the Camera Connection Kit (with older iOS devices), or the Lightning cable with the very newest iOS devices.
The iPod Classic will only handshake with MFi equipped USB Type A ports, meaning you use a standard 30-pin cable to connect to the Classic's dock port, and the other end needs a Type A input with authentication chip.
Even the Oppo HA-2, despite having such a Type A MFi port does not list the Classic as a compatible model, however it does work. I asked Oppo why they don't officially list the Classic as a supported model and they said the authentication chip it uses is slightly older/different to what is used in iOS, and they can't guarantee proper performance though they conceded it does in fact work.
In practice I haven't had any problem with the Classic and HA-2, but Oppo said the specific issue is the actual initial connection and handshake, it can be finicky because the HA-2 has one generation newer authentication than the Classic does, it is meant to be used with iOS and thats all they guarantee will work.
Back to the Mojo, it is like just about any other USB DAC in that it doesn't have the MFi Type A input, just a standard USB input. That means it will only work with older iOS devices using the CCK, or newer ones using Lightning, each of which operates in USB Host mode with those connections (essentially an OTG connection but Apple doesn't call it that).
As far as any Lightning adapter goes? I'm not sure what you mean, there isn't any Lightning port on either the Mojo or the Classic, no?