  We show that on a Riemann surface lamination locally embedded in
$\mathbb{C}^2$, $C^1$ functions (in the sense of the $C^1$ structure of the
lamination) are uniform limits of ambient $C^1$ functions, with $L^p$ control
on the derivatives along the leaves. This implies that locally in $C^2$, a
(1,1) positive closed current dominated by a uniformly laminar current is
itself uniformly laminar.
