That kind of chaos is about simple systems that are unpredictable in the long term. That Lorenz system is just a few equations you could write on a napkin. Whereas your brain has billions and billions of neurons. (You might blame the complexity on having a lot of parts.)

That said, another aspect of dissipative chaos is that a highly complex system like turbulence (10^28 or so atoms bouncing off each other) often can be described by an attractor that is rather low dimensional and could be modeled with a few equations. So you might have some neural signal that tools like that could make an interesting model of.