Whether it's for handling your business's social media account or just for personal reasons, like trolling an ex-girlfriend's page (not that I've ever done that) or posting on behalf of your pup, there are instances where having two different Facebook accounts on one device is simply easier than switching back and forth.
While Facebook may not include a native feature to manage separate accounts like Twitter does, there is a simple method to sign into two different Facebook accounts at once on a single Android device.
After testing Facebook Lite, I soon realized that I was receiving duplicate notifications on my account; one from the official Facebook app and one from Facebook Lite. Clearly each app was running independently of the other, which means that they could accept different login credentials.
Lite still isn't available on the Google Play Store in the States, but you can still grab the Facebook Lite APK here. (Make sure "Unknown sources" is enabled on your device before trying to install it.)
Granted, you could always sign in with a different account if you use the web version of Facebook, but with two apps, you have the advantage of getting notifications directly to your device for both accounts. Just sign into Lite like you would Facebook and enjoy the coexistence of both apps.