Here is a link to a site that states the Pica (eating dirt,rock etc.) are common in dogs with esophageal issues. You dog may not be lacking anything, just a side effect of ME.

The medical term for eating dirt, rocks, or any other non-food materials is pica. Eating non-food materials may be associated with behavioral issues or health disorders. Some veterinarian experts believe that chewing on non-food materials starts when puppies are weaned too early or too abruptly. Many veterinarian specialists associate pica with the following health disorders:

Consult with your veterinarian about your pet’s possible health problems. He or she may suggest changing your pet’s diet or supplementing it with approved minerals, vitamins or enzymes. If all health disorders have been ruled out, then behavioral reasons for pica should be considered. Your dog or puppy may eat dirt, or pick up a rock just to gain your attention, or because he is bored or was encouraged and trained to pick up objects. Some cases need medical treatment with behavior modifying drugs.