This is an adapted version of the original DmxSimple library that works with the Lithne boards.
You can download the library here. It also comes with some examples of how to use it.
The Lithne DMX Shield has the dmxPin connected to D11, so call DmxSimple.usePin(D11); in your setup().
nb: This library is compatible both with Lithne and regular Arduino's, however when using a regular Arduino, you can use only up to channel 80.
nb2 - if you have problems: The timing with this library appears to be rather critical, so critical that it may be different for different Lithne boards. In case of weird behaviour (flickering) you can alter the number of cycles that the processor idles to create the 4us delay that is used to create a DMX bit. This is found in the library and is currently 36, but used to be 35. Additionally, you may want to alter the 40 or 41 cycles used to create the frame's start bit.