  Recently, in the metric spaces, Le Donne and the author introduced the
so-called intrinsically Lipschitz sections. The main aim of this note is to
adapt Cheeger theory for the classical Lipschitz constants in our new context.
More precisely, we define the intrinsic Cheeger energy from $L^2(Y,\R^s)$ to
$[0,+\infty],$ where $(Y,d_Y,\mm)$ is a metric measure space and we
characterize it in terms of a suitable notion of relaxed slope. In order to get
this result, in more general context, we establish some properties of the
intrinsically Lipschitz constants like the Leibniz formula, the product formula
and the upper semicontinuity of the asymptotic intrinsically Lipschitz
constant.
