Sample code / workflow would be helpful.
If you want to interact with a external LED display through Android phone then you have two following options
Using serial of Android phone. In the market you can easily find Bluetooth to Serial converter modules. Once you connect with these bluetooth module from your Android phone then you can easily send text to that modules line serial port data. then again it will be dilivered to the LED display again connected to that external module via serial link. But in that case your display module should be capable enough to communicate with Serail RS232 link.
Using SMS interface from Android phone. Second option is much easier like sending an SMS form a Android phone application. For that you have to buy a SMS enabled LED display. And then start sending SMS having your text message to that Display and all that text will be displayed on that LED Sign. Such display are called "SMS based LED Display" or "SMS based LED Sign" sometime "programmable LED Sign". below are some external links for such product:
Sometimes these screens also worked on Live streaming protocols and known as led stock ticker
http://www.ledsignsdisplays.com/led-ticker-a-data-screens/stock-tickers
http://www.photonplay.com/sms-based-led-display-board-signs.html