Summary: In [A. Avila and R. Krikorian, Invent. Math. 202, No. 1, 271–331 (2015; Zbl 1356.37070)], the authors considered analytic monotonic cocycles, and showed that the Lyapunov exponent of an analytic family of analytic monotonic cocycles is analytic. We extend the result of [loc. cit.], and show that a analytic family of meromorphic monotonic cocycles have analytic Lyapunov exponent. We then consider the quasiperiodic Schrödinger operators that have meromorphic monotone potentials. Since the associated Schrödinger cocycles are meromorphic and monotonic, by applying the result we show that the Lyapunov exponent of the associated Schrödinger cocycle is analytic. For the proof we rely heavily on the techniques in [loc. cit.].