Is there a link between autoimmune diseases and X-chromosome inactivation?
Yes, here is an article on it: "The role of X-chromosome inactivation in female predisposition to autoimmunity"

Below see the method and results summarised. 


  Using a DNA methylation assay, we have examined the X-chromosome
  inactivation patterns in peripheral blood from normal females (n =
  30), female patients with a variety of autoimmune diseases (n = 167).
  No differences between patients and controls were observed. However,
  locally skewed X-chromsome inactivation may exist in the thymus, and
  therefore the underlying hypothesis remains to be disproved.