Unlike iOS devices by default most Android tablets do not have a "never sleep" display setting, which of course means your Android tablet will keep falling asleep while installed into your lilitab.
There are a number of ways around this however, either by installing an app or changing a setting that can be a bit hard to find.

In Settings if you scroll down towards the bottom directly under "Accessibility" you should see a "Developer Options" section (this may be located inside the "Apps" section on some tablets).
Inside this there is a Setting called "Stay Awake".
Enable this and your tablet will no longer fall asleep on you 😉

Alternately there a few apps you can use to control your tablet's sleep conditions.
We prefer RedEye, it allows you to set your tablet to not sleep when connected to wall power and also wake up when connected to wall power. When configured properly RedEye will enable your tablet to turn on when plugged into wall power, remain awake while plugged in and when unplugged from the wall fall asleep.
You can find the app here for $0.99 (the free version throws up some ads so we recommend you shell out the $0.99 for the paid version).