  The paper deals with dynamics of expanding Lorenz maps, which appear in a
natural way as Poincar\`e maps in geometric models of well-known Lorenz
attractor. Using both analytical and symbolic approaches, we study connections
between periodic points, completely invariant sets and renormalizations. We
show that some renormalizations may be connected with completely invariant sets
while some others don't. We provide an algorithm to detect the renormalizations
that can be recovered from completely invariant sets. Furthermore, we discuss
the importance of distinguish one-side and double-side preimage. This way we
provide a better insight into the structure of renormalizations in Lorenz maps.
These relations remained unnoticed in the literature, therefore we are
correcting some gaps existing in the literature, improving and completing to
some extent the description of possible dynamics in this important field of
study.
