Yes, LGs will work with Macs. Have you installed and run the script I linked for you? (you did not say) What I suspect is happening is the following:
1. Your iBook's standard configuration is to only mirror the internal monitor rather than allow for a second independent monitor.
2. As such, your iBook's default resolution does not match a resolution that your LG monitor is set to display (particularly since your iBook's screen is not widescreen and the LG's is).
3. Thus, you have a black screen.
This limitation formerly was overcome by using a "spanning hack." (Google it, I don't know the details). But now, I believe the script I have linked for you eliminates the need for the spanning hack (meaning to hack your firmware--that much I do know).
Solution? Read my other post and install the script I linked at the end of the post. If that does not work, you likely have a hardware problem or adapter problem or you need to do the old-fashioned "spanning hack." (
http://www.macaddict.com/forums/topic/44990)