How do the Gamemakers drive the tributes towards the lake and why does Katniss believe that they are doing so?

Gamekeepers drive tributes to the lake by making the difficulties like fire or drying out the water. Katniss knows this because they control everything, and they also need to produce excitement for the audience.

Explanation:

Gamekeepers create various troubles and difficulties for the tributes in order to drive them to the same place. One of these difficulties is the fire that starts surrounding Katniss. It is so large, that she knows it is synthetically made, which means by Gamekeepers. Later on, Katniss and Peeta are also driven to the lake by the fact that all other water sources have been dried up and this proves to be the only place to get the water.

Katniss is sure of this because she already knows the way Hunger Games work. The Gamekeepers must make the games interested to the audience, which includes direct combat with other tributes. She realizes these are all events that do not happen naturally but are made by Gamekeepers as the arena is also made and controlled by them completely.