We define a group theoretic criterion on a pro-$p$ group that guarantees the existence of an analytic structure over ${\mathbb Z}_p[[t]]$. This is a one-way analogue of Lazard's succesful answer to the $p$-adic version of Hilbert's Fifth Problem. In the course of the proof we define a $T$-map, a $T$-uniform group and set up a category equivalence between $T$-uniform pro-$p$ groups and powerful ${\mathbb Z}_p[[t]]$-Lie algebras.