  In this paper we determine, under some mild restrictions, the lattice of
submodules $\gL$ of a module $M$ all of whose composition factors have
multiplicity one. Such a lattice is distributive, and hence determined by its
poset of down-sets $P$. We define a directed Ext graph $\Ext_\gL$ of $\gL$ and
show that if $\Ext_\gL$ is acyclic, then $\Ext_\gL$ determines $P$. The result
applies to multiplicity free indecomposable modules for finite dimensional
algebras with acyclic Ext graph. It also applies to some deformed Verma modules
which arise in the Jantzen sum formula basic classical simple Lie superalgebras
in the deformed case.
