  Let $\Bbbk$ be a field of characteristic zero and let $\mathbb{W}_n =
\operatorname{Der}(\Bbbk[x_1,\cdots,x_n])$ be the $n^{\text{th}}$ general
Cartan type Lie algebra. In this paper, we study Lie subalgebras $L$ of
$\mathbb{W}_n$ of maximal Gelfand--Kirillov (GK) dimension, that is, with
$\operatorname{GKdim}(L) = n$.
  For $n = 1$, we completely classify such $L$, proving a conjecture of the
second author. As a corollary, we obtain a new proof that $\mathbb{W}_1$
satisfies the Dixmier conjecture, in other words,
$\operatorname{End}(\mathbb{W}_1) \setminus \{0\} =
\operatorname{Aut}(\mathbb{W}_1)$, a result first shown by Du.
  For arbitrary $n$, we show that if $L$ is a GK-dimension $n$ subalgebra of
$\mathbb{W}_n$, then $U(L)$ is not (left or right) noetherian.
