Lightroom license from different devices

You are licensed for one person to use the desktop software, on up to two devices. The mobile software can be used on other devices besides those two.

Business use is allowed, as well as personal use, provided this is by the licensed person.

The desktop software can be installed on more than two devices, but only two at a time can be successfully signed-in for your Adobe account (it keeps track). You do not need to sign out each session on the device, you can leave that signed-in - and you do not need continuous internet access: the sign-in can "last" for up to 90 days since it last was able to communicate with Adobe. You can reset signins using the web console of your Adobe account (for example, if a computer that was signed in became unusable, or was stolen) so that your two allowed sign-ins would both again become available.

Photoshop will not start unless you are signed in on the device. Lightroom Classic will start but only in a functionally restricted mode. Lightroom (Cloud) and the mobile software apps require sign-in in order to connect to your data. 

Your software license for Lightroom Classic and Photoshop allows you to install and active the software on two computers, for your own personal use, as long as the software is only in use on one computer at a time.