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

Intrinsic Lipschitz sections of no-linear quotient maps