Regularity for almost minimizers of a one-phase Bernoulli-type functional in Carnot Groups of step two

We prove that nonnegative almost minimizers of the horizontal Bernoulli-type functional $$J(u,\mathrm{\Omega }):={\int }_{\mathrm{\Omega }}(\mathrm{\mid }{\mathrm{\nabla }}_{\mathbb{G}}u(x){\mathrm{\mid }}^2+{\chi }_{\{u>0\}}(x))dx$$ are Lipschitz continuous in the intrinsic sense.