While I cannot publish my example, the general idea when it comes to integrating TCP/IP stack of your choice with its PPP driver is the same among all serial modems and all TCP/IP stacks that I've worked with.
Generally as you've mentioned, you start with configuring the modem using AT commands - things like checking whether SIM card is present, whether it requires PIN, specifying PIN if needed, checking if it has successfully registered in the network. Possibly reading additional information data such as IMEI, IMSI as well as diagnostic data: signal quality, BER etc. Once you're done, you switch the modem to "data" mode (see ATD*99), wait for the modem to respond to that command and pass the responsibility to the TCP/IP stack, as at this point the modem starts talking PPP.
When it comes to integrating your modem with the stack so it can communicate with it, the implementations I've encountered all require implementing some form of low-level API functions for the stack. For LwIP, the wiki page you've linked in the "PPP over serial" section, it is described quite well how those functions should behave. Because TCP/IP stacks are just a software library not tied to specific hardware and they can be run on almost anything (assuming sufficient resources), specific API implementations such as the one discussed are not always provided - there would have to be a ton of examples for it to provide any value. Although if you google around for it, you might find someone having done it for the MCU that you use personally. Assuming you've already done the part where you successfully comminicate with your modem using AT commands, it shouldn't be much more other than using the send/receive functions you already have. Some slight changes may be required, such as adjusting their behavior (synchronous->asynchronous or vice versa) or redirecting received data to the TCP/IP API receive function instead of your AT command parser. Nonetheless, most of the necessary hard work should be done already.
Once the TCP/IP stack takes over, you continue with the modem using provided stack PPP API. For LwIP see functions such as: pppSetAuth, pppOverSerialOpen. Those will cause the stack to internally handle the necessary communication with the modem over PPP: LCP, PAP/CHAP, IPCP. Once that part is done (you retrieve IP configuration data from the network) it becomes transparent how this operates - it becomes one (of possibly multiple) network interfaces and you use it just as any other one, for example using socket API.
