\lambda is the 'flux limiter'. It comes into the equations in the diffusion term:

\frac{\partial E}{\partial t} = \nabla \cdot (\frac{c \lambda}{\kappa_R \rho} \nabla E)

This is because instead of solving the following conservation equation,

\frac{\partial E}{\partial t} =- \nabla \cdot F

(which would require an additional equation for F), we make the 'flux-limited' approximation that,

F=-\frac{c \lambda}{\kappa_R \rho}\nabla E

This then turns the conservation equation into a diffusion equation:

\frac{\partial E}{\partial t} = \nabla \cdot (\frac{c \lambda}{\kappa_R \rho} \nabla E)

The value of \lambda controls whether the radiation is diffusing in the free-streaming limit (\lambda \rightarrow 0), i.e. at the speed of light, or is diffusing as it would in the optically thick limit (\lambda \rightarrow \frac {1}{3}). The FLD approximation does well at these two limits, but not in between. Let's examine these two limits in more detail and then consider why it doesn't perform as well in between.