$p$-adic completed group ring of $\mathbb{Z}_l$

Question

Let $G$ be a profinite group. Recall the complete group ring is defined as $\mathbb{Z}_p[[G]]:=\varprojlim_U\mathbb{Z}_p[G/U]$ where $U$ runs over all open normal subgroups of $G$. When $G=\mathbb{Z}_p$, this ring plays an important role in Iwasawa theory and by choosing a topological generator $\gamma$ of $G$, we can establish a topological isomorphism $\mathbb{Z}_p[[G]]\to \mathbb{Z}_p[[T]]$ (ring of formal power series) via $\gamma\mapsto 1+T$. This leads me to wonder what happens for $\mathbb{Z}_p[[\mathbb{Z}_l]]$, where $l\neq p$ is a prime number. Is there any similar description in terms of power series ring?