Conditions on a bounded Euclidean domain for the Lebesgue measure to be doubling

Question

Let $\Omega \subset \mathbb{R}^n$ be an open, bounded subset of a Euclidean space. Under what regularity conditions of the boundary of $\Omega$ the Lebesgue measure $\mu$ is known to be a doubling measure, i.e., it admits a constant $C>0$ (dependent only on $\Omega$) such that $\mu(\Omega \cap B(x,2r))\leq C\mu(\Omega \cap B(x,r))$ for all $x \in \Omega$ and $r>0$. I have read that "it is well-known" that the Lebesgue measure is a doubling measure on any domain with a Lipschitz boundary, but have found it extremely hard to find a precise theorem/proof of such a statement anywhere.