  We study the deformations of a wide class of Yang-Baxter (YB) operators
arising from Lie algebras. We relate the higher order deformations of YB
operators to Lie algebra deformations. We show that the obstruction to
integrating deformations of self-distributive (SD) objects lie in the
corresponding Lie algebra third cohomology group, and interpret this result in
terms of YB deformations. We show that there are YB operators that admit
integrable deformations (i.e. that can be deformed infinitely many times), and
that therefore give rise to a full perturbative series in the deformation
parameter $\hbar$. We consider the second cohomology group of YB operators
corresponding to certain types of Lie algebras, and show that this can be
nontrivial even if the Lie algebra is rigid, providing examples of nontrivial
YB deformations that do not arise from SD deformations.
