We consider MRL maps (Markov-Renyi-Luroth), a class of interval maps with infinitely many branches that can have parabolic fixed points. We prove that for every MRL map T, the Lyapunov spectrum can be expressed in terms of the Legendre transform of the topological pressure of -t log |T'|, generalizing previous results in the area. We also show that the Lyapunov spectrum coincides with a function directly related to the Newton-Raphson method applied to the topological pressure of -t log |T'|.