  In this paper we study the lattice of restricted subalgebras of a restricted
Lie algebra. In particular, we consider those algebras in which this lattice is
dually atomistic, lower or upper semimodular, or in which every restricted
subalgebra is a quasi-ideal. The fact that there are one-dimensional
subalgebras which are not restricted results in some of these conditions being
weaker than for the corresponding conditions in the non-restricted case.
