This is a slightly delayed answer, but since the theory of lightning is still under development, there should be no harm in speculating about it a bit more.
As was mentioned in other answers, a lighting between a cloud and the ground typically starts at a cloud as a negative current heading downwards.
Let's look at it in more detail.
First, we need to understand where these negative charges are coming from?
Those charges are not likely to be free electrons and are not likely to be water molecules: they are negative ions of air molecules. There are always a few of negative and positive ions floating around, but when they are sped up by the field created by a charged cloud, they split neutral air molecules and can initiate a chain reaction that ionizes the air along the field lines.
While the negative ions are rushing toward the ground, making more ion pairs along the way, the positive ions rush back toward the cloud doing pretty much the same thing. But while the negative ions have a long way to go, the positive ions start returning to the cloud and neutralizing the charge in the cloud as soon as the process begins.
As the cloud gets neutralized around the origin of the lighting, new charges from other parts of the cloud are rushing in to keep things going. But they are not going to arrive instantaneously, so we could speculate that the field pushing the leader out will weaken a bit following the initial burst. Perhaps this could cause the leader to pause and wait until the charge at its origin in the cloud is replenished. I am not claiming that this is the explanation of the bursty nature of the leader, but just making an observation.
Since, as we are suggesting, the current of the leader is formed by air molecules moving upward and downward and making a lot of collisions, we could expect that this fast moving air (wind) will create a lot of turbulence around its path.
With that in mind, it is only natural that some of the ions could stray from the straight path and, if they are energetic enough, could possibly initiate alternative paths.
So, even if the air was perfectly uniform before the lighting got started, it will be thoroughly disturbed as the lightning progresses, creating multiple opportunities for branching.
I don't know if branching tends to occur at the end of the "steps", but if it did, it would not be illogical, since the arrival of a new wave of energy could require multiple outlets.