  We consider MRL maps (Markov-Renyi-L\"uroth), 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 $-t\log|T'|$.
