Lillypad has the same interface pins available as a standard arduino so anything that works
with a typical Arduino board will also work with a Lilypad.
But in terms of "Biggest" there is no limit. If you have enough dollars you could interface
the Lilypad with something as large as a FootBall stadium jumbotron using messages over
a serial port.
It isn't clear what you are wanting/needing since you have not specified any parameters
such as cost targets, needed pixel geometries, voltages (3v vs 5v), interfaces needed (serial, parallel etc) etc...
Here are two libraries that can be used on fairly inexpensive LCDs that are readily available:
glcd:
http://www.arduino.cc/playground/Code/GLCDks0108
http://code.google.com/p/glcd-arduino/
u8glib:
http://code.google.com/p/u8glib/
And then there are ready made solutions such as:
--- bill