"Infernal Affairs 3" makes things clear. Lau finds out that there are five gang moles in the police force, and one of them is supposedly killing the others to conceal his identity. Lau decides that he has to be the survivor. We see him spying on Superintendent Yeung from the police force's "security department", whatever that is. At first I had the impression that he was one of the moles, but as the film progresses it becomes clear that he's a "good cop", the embodiment of what Lau wants to be. Then, as the film comes to a close, Lau goes into a mental meltdown. He begins to think that he is the police mole Chan. This follows up from themes from the original film, the mental stress of having to spend years pretending you're someone you're not.
It was difficult for me to understand the beginning of the film. I didn't understand everything that was happening, and even when I did understand things I didn't understand their relevance. I have a feeling that if I watch the trilogy again I might understand and enjoy it more.