A continuous lattice is a complete lattice $L$ in which every element $y$ is equal to $\bigvee${$x \in L \mid x \ll y$} where $x \ll y$ ("x approximates y" or "x is way below y") if for any directed set $D \subseteq L$, $y \leq \bigvee D$ implies that there is a $d \in D$ such that $x \leq d$.

It is known that the set of projections in an arbitrary W\*-algebra is a complete orthomodular lattice. I would like to know for which kind of W\*-algebras this lattice is also continuous.