Laz might have been oblivious to the plot set against him, but he wasn't oblivious to what happens to his body. For instance, when you are focused on something, you might be able to tune everything else out. Heavy sleepers are a good example. It would take something like a loud fire alarm or their house collapsing for them to wake up. In this case, although it wasn't apparent to Laz at first, it didn't mean he didn't notice it shortly after it happened.
As it was, Laz was in the middle of watching the fight when he felt a strange itch in his stomach. It kind of felt like indigestion although it was more like concentrated on one spot. Normally, a poison starts acting as soon as it's ingested, making it's way quickly to the blood stream. But that would be the effect for a normal person. Laz was anything but.
