  In this work we establish the optimal Lipschitz regularity for non-negative
almost minimizers of the one-phase Bernoulli-type functional $$
\mathcal{J}_{\mathrm{G}}(u,\Omega) := \int_\Omega \left(\mathrm{G}(|\nabla
u|)+\chi_{\{u>0\}}\right)\,dx $$ where $\Omega \subset \mathbb{R}^n$ is a
bounded domain and $\mathrm{G}: [0, \infty) \to [0, \infty) $ is a Young
function with $\mathrm{G}^{\prime}=g$ satisfying the Lieberman's classical
conditions. Moreover, of independent mathematical interest, we also address a
H\"{o}der regularity characterization via Campanato-type estimates in the
context of Orlicz modulars, which is new for such a class of non-standard
growth functionals.
