  In this paper we continue the study of the subalgebra lattice of a Leibniz
algebra. In particular, we find out that solvable Leibniz algebras with an
upper semi-modular lattice are either almost-abelian or have an abelian ideal
spanned by the elements with square zero. We also study Leibniz algebras in
which every subalgebra is a weak quasi-ideal, as well as modular symmetric
Leibniz algebras.
