I would love to know if it's possible to access the octoprint server (via octopi.local or 192.168.0.22) on mobile data (i.e. 4G). I thought it would work but it turns out that I cannot connect to the server.
Is it possible to connect on mobile data, if so I would love to know how, or do I require a LAN (etc.) connection?
Thanks.
Your printer is connected to your local area network (LAN) and has a private class C IP address (192.168.0.22). Mobile data (4G) is a cellular service (WAN) and to connect to your printer from that WAN you will need to configure your LAN router (the box that connects your LAN to the internet (WAN). There are security issues that need to be understood and addressed when you do this.
I'm guessing the device you have with 4G capabilities is a cell phone. Most cell phones can also use WiFi and if you have it either in your router or as an access point on your LAN, you can then connect your phone to your printer when you are in WiFi range of your LAN.
There are multiple threads on these forums that discuss connecting to a printer from the internet. Do a little searching to gain some understanding of the issues and then if you need to, ask some more detailed questions. Remember the more you tell us, the better we can answer.
Yes, it's possible. I used to have an app, but, it seems that an android update removed it on me...
Oh, here's a new one. It's called Printoid. I found it on google's playstore, and it lets you conect to your Octo from outside your LAN. It looks pretty, but I haven't fully tested it yet. There are ads on the free version
Here's another one, it's called OctoRemote. But, it only works inside your LAN. Looks nice
Niether one seems to be able to let me implement GPIO switches so that I can turn my lights on and off, but, there's something in Octoremote that says "controls" that lets you add a script. That might work
And then there's the third option, which is not recommended, which is to put your Octo's IP address into your routers gaming section, and open it up to the internet. But, again, it's a bad idea unless you really know what yer doing and feel safe opening up your printer to potential criminals who would probably want to use the Octopi server to host pr0n and viruses
On the other hand, you COULD get some free pr0n out of it 
It looks to me like Printoid is your best option if you want to be able to access your printer from outside your house with your android based phone
For what it's worth, I wrote a Robo-branded mobile phone interface for OctoPrint which uses PhoneGap to serve up the mobile interface. In theory, one could serve up this from a Raspberry Pi Zero W computer there at home and it seems to be a better interface for smartphones with limited screen real estate.
It's open-sourced.