|If the web server presently is only connected to the private LAN then there's really no way to access it from outside right now.|
From the sounds of it, you have a "combo unit" between your LAN and the internet. Combo unit being a device that is a combination modem, router, and wireless access point. If this is correct (feel free to correct me if it's not, but do include the make/model of the device you're using), you'd have to connect the web server to that device in order to have external connectivity to it.
I would suggest you do the same thing you did with your other server, that is, use two network interfaces and have one connected to the private LAN, and the other to your external device.
Once you've done that, you can then put the web server in the DMZ, if your router has DMZ capability, to allow external access.
If your router doesn't do DMZ, you could create a port forward on the router to allow external access.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.