How do I replace the latch?

That's a tough repair - you will need to replace the display bezel, which requires almost a complete tear down of the machine.

Unfortunately, it does not look like iFixit carries the exact part you need. I did find one here, however:

http://www.powerbookmedic.com/xcart1/pro...

This is an issue I would serious consider just living with, as the 12" Powerbook G4 is one of the most difficult models to work on, requiring an incredible amount of patience and care, as the parts are small, easily deformed, and very tightly put together.