  We continue our studies of the correspondence between 4d $\mathcal{N}=2$
SCFTs and 2d W-algebras. The purpose of this paper is to study the relationship
between 2d lisse W-algebras and their 4d SCFT partners. The lisse W-algebra is
the W-algebra whose associated Zhu's $C_2$ algebra is finite dimensional. As
the associated variety of Zhu's $C_2$ algebra is identified with the Higgs
branch in the 4d/2d correspondence, the lisse condition is equivalent to the
absence of the Higgs branch on the 4d side. We classify 4d $\mathcal{N}=2$
SCFTs which do not admit Higgs branch, then these theories would give lisse
W-algebras through the 4d/2d correspondence. In particular, we predict the
existence of a large class of new non-admissible lisse W-algebras, which have
not been studied before. The 4d theories corresponding to lisse W-algebra can
appear in the Higgs branches of generic 4d $\mathcal{N}=2$ SCFTs, therefore
they are crucial to understand the Higgs branches of $\mathcal{N}=2$ SCFTs.
