  In this paper we establish an optimal Lorentz estimate for the Riesz
potential in the $L^1$ regime in the setting of a stratified group $G$: Let
$Q\geq 2$ be the homogeneous dimension of $G$ and $\mathcal{I}_\alpha$ denote
the Riesz potential of order $\alpha$ on $G$. Then, for every $\alpha \in
(0,Q)$, there exists a constant $C=C(\alpha,Q)>0$ such that \begin{align} \|
\mathcal{I}_\alpha f \|_{L^{Q/(Q-\alpha),1}(G)} \leq C\| X \mathcal{I}_1 f
\|_{L^1(G)} \end{align} for distributions $f$ such that $X \mathcal{I}_1 f \in
L^1(G)$, where $X$ denotes the horizontal gradient.
