I don't see that sending the data is a problem - since you only send it one byte at a time, it doesn't really matter how much you want to send. But it sounds as if you plan to generate that data at runtime on the Arduino, and that implies you need to be able to store the whole thing somewhere persistent. As SD card would be the easiest choice in my opinion - it also means you have the option of view and altering the data on a PC if required for test purposes. If you are willing to involve a PC in your solution then you can offload any or all of the google lookup, conversion to LED control sequence and persistent storage to the PC. If this is intended to be a mobile device, that might not be practical though.