  We investigate whether 4-dimensional static and cosmological Lifshitz
solutions can be found from deforming the existing (A)dS_4 compactifications in
IIA and IIA* supergravity. Using a well motivated compactification Ansatz on
SU(3)-structure manifolds with 19 undetermined parameters we demonstrate that
this is not the case in ordinary IIA supergravity, thereby generalising
previous nogo results in different ways. On the other hand, for IIA* we
construct explicit cosmological Lifshitz solutions. We also consider solutions
with non-constant scalars and are able to find simple static and cosmological
Lifshitz solutions in IIB* supergravity and a Euclidean Lifshitz solution in
ordinary Euclidean IIB supergravity, which is similar to a non-extremal
deformation of the D-instanton. The latter solutions have z=-2.
