Is it possible that anorexia/eating disorders are more likely to be found and associated with pathological lying , could they be closely related?

They can be co-: morbid; that is, co-exist at the same time. Lying to cover up a problem is common, as in addictions, and eating disorders are shameful for many, so also are covered up. Pathological lying is more complicated and is found more in impulsive and other personality disorders. This behavior doesn't necessarily need an addiction or eating disorder to manifest.