Cannot join world's on local LAN MPE 0.13.1
Joining a server on your local network (WiFi)
You first need to open Minecraft on both devices, turn off multiplayer game in options, open a world, then leave that world again, and turn on multiplayer game in options. This should hopefully reset multiplayer broadcasting, so it should work.
If that doesn't do anything, quit Minecraft on both devices. On your home screen, double tap the home button and end Minecraft by swiping up all the apps (all iOS users probably know this). Then, once again on the home screen swipe up from the bottom of the home screen (from the top if on android) and enable airplane mode on both devices. After ten seconds disable airplane mode, connect to your network and open Minecraft ONLY on the device on which the world is saved on. Wait and other ten seconds and disable airplane mode. Open Minecraft as normal, and you should be able to join.