  This note concerns low-dimensional intrinsic Lipschitz graphs, in the sense
of Franchi, Serapioni, and Serra Cassano, in the Heisenberg group
$\mathbb{H}^n$, $n\in \mathbb{N}$. For $1\leq k\leq n$, we show that every
intrinsic $L$-Lipschitz graph over a subset of a $k$-dimensional horizontal
subgroup $\mathbb{V}$ of $\mathbb{H}^n$ can be extended to an intrinsic
$L'$-Lipschitz graph over the entire subgroup $\mathbb{V}$, where $L'$ depends
only on $L$, $k$, and $n$. We further prove that $1$-dimensional intrinsic
$1$-Lipschitz graphs in $\mathbb{H}^n$, $n\in \mathbb{N}$, admit corona
decompositions by intrinsic Lipschitz graphs with smaller Lipschitz constants.
This complements results that were known previously only in the first
Heisenberg group $\mathbb{H}^1$. The main difference to this case arises from
the fact that for $1\leq k<n$, the complementary vertical subgroups of
$k$-dimensional horizontal subgroups in $\mathbb{H}^n$ are not commutative.
