  We compute the homotopy derivations of the properads governing even and odd
Lie bialgebras as well as involutive Lie bialgebras. The answer may be
expressed in terms of the Kontsevich graph complexes. In particular, this shows
that the Grothendieck-Teichm\"uller group acts faithfully (and essentially
transitively) on the completions of the properads governing even Lie bialgebras
and involutive Lie bialgebras, up to homotopy. This shows also that by contrast
to the even case the properad governing odd Lie bialgebras admits precisely one
non-trivial automorphism - the standard rescaling automorphism, and that it has
precisely one non-trivial deformation which we describe explicitly.
