$\begin{align*}L = \hbar \sqrt{l \left(l+1 \right)}\end{align*}$
so $l = 1$ in this case. So, the possible values of $m$ are $-1$ , $0$ , and $1$ .
$\begin{align*}L_z = \hbar m\end{align*}$
so, the possible values of the $L_z$ are
$\begin{align*}\boxed{-\hbar, 0, \hbar}\end{align*}$
Therefore, answer (D) is correct.

Solution to 2008 Problem 64