  We identify a large class of Orlicz spaces $X$ for which the topology
$\sigma(X,X_n^\sim)$ fails the C-property introduced in [7]. We also establish
a variant of the C-property and use it to prove a $w^*$-representation theorem
for proper convex increasing functionals on dual Banach lattices that satisfy a
suitable version of Delbaen's Fatou property. Our results apply, in particular,
to risk measures on all Orlicz spaces over $[0,1]$ which is not $L_1[0,1]$.
