In this paper, we prove that the lattice of all closure operators of a complete Almost Distributive Lattice L with fixed maximal element m is dual atomistic. We define the concept of a completely meet-irreducible element in a complete ADL and derive a necessary and sufficient condition for a dual atom of Φ(L) to be complemented.This research is supported by the U.G.C, Major Research Project Ref. No.41783/2012(SR) 17-07-2012