  Le Donne and the author introduced the so-called intrinsically Lipschitz
sections of a fixed quotient map $\pi$ in the context of metric spaces.
Moreover, the author introduced the concept of intrinsic Cheeger energy when
the quotient map is also linear. In this note we investigate about the non
linearity of $\pi$. In particular, we find a Leibniz formula for the intrinsic
slope when $\pi$ satisfies a weaker condition. After that, we focus our
attention on Carnot groups and using the properties of intrinsic dilations we
show that the dilation of a Lipschitz section is so too. Finally, in Carnot
groups of step 2, we give a suitable additional condition in order to get the
sum of two intrinsically Lipschitz sections is so too.
