I don't know if this helps you at all, but when I used Linux I had it set up so that once my phone was out of Bluetooth range of about ten feet, it would lock the screen and turn it into sleep mode (the monitor, not the comp), and once it detected my phone in the room again, it turned the screen back on and unlocked the system. It wasn't an Android phone, just a regular old-fashioned dumb phone with Bluetooth, and the OS was Linux Mint. I don't remember the name of the app that enabled this feature, but it was free and I got it from the Mint App Library.
If you're looking to actually access the computer, then probably a VPN would be the way to go, or something like TeamViewer.