Can chronic eczema be a sign of lupus, especially with a family history of lupus?

No! Eczema is not associated with lupus. In my practice I have many patients with psoriasis & eczema with positive anas.They do not have arthritis, and clearly not lupus or related disease. On the other hand, both eczema and psoriasis affect 10% of the population. With that, one would think that 10% of sle patients have these skin diseases, but though common, just by chance, but they are not related.
More than rash. Lupus is a multisystem disease that may include a rash. Family history is quite important. Diagnosis involves a thorough physical exam and blood work.