The setOutputHander() function tells Bitlash: "Here is the function you should use to print an output character." You pass it a function that takes a single character as an argument. Your function takes the character and does whatever you like with it: print it to an LCD, send it over the internet, save it to EEPROM, whatever.
There is an example showing how to use setOutputHandler in the "loudbitlash" example folder. The example simply makes every printed character uppercase. Instead, you could replace the uppercasing code with code to print to your lcd.
There is also a serial LCD example that may be more appropriate for the topic of this thread.
Have a look at the examples and see if that helps puzzle it out.