A lattice is called *adiamond* if it admits no sublattice equivalent to the diamond lattice $M_3$ below:

The top interval of a lattice is the interval between the meet of all the maximal elements and the greatest element. A lattice is called selftop is it is equal to its top interval.

Let $\mathcal{L}$ be a selftop finite lattice, $M$ the set of its maximal elements, and $e$ the smallest element.

Question: Is $\mathcal{L}$ adiamond iff $\forall S \subsetneq M$, $\bigwedge_{b \in S}b >e$?