  It is well known that the Liverani-Saussol-Vaienti map satisfies a central
limit theorem for H\"older observables in the parameter regime where the
correlations are summable. We show that when $C^2$ observables are considered,
the variance of the limiting normal distribution is a $C^1$ function of the
parameter. We first show this for the first return map to the base of the
second branch by studying the Green-Kubo formula, then conclude the result for
the original map using Kac's lemma and relying on linear response.
