  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. We study connections between periodic points, completely invariant
sets and renormalizations. We show that in general, renormalization cannot be
fully characterized by a completely invariant set, however there are various
situations when such characterization is possible. This way we provide a better
insight into the structure of renormalizations in Lorenz maps, correcting some
gaps existing in the literature and completing to some extent the description
of possible dynamics in this important field of study.
