I'm sorry to hear of this with your Lhasa. The ultimate cause of coprophagia in adult dogs has always been elusive. Some feel that the problem is behavioral, while others are convinced there is an organic reason. Soft stools, incomplete digestion of food within the stools, evidence of steatorrhea (fat in the feces), increased stool frequency or volume, or a voracious appetite ("very greedy") might indicate a problem with maldigestion (a failure of her pancreas to produce enough digestive enzymes) or malabsorption (a failure to efficiently absorb digested food). Other gastrointestinal disturbances such as inflammatory bowel disease, systemic health problems including renal failure and endocrinopathies, medications such as glucocorticoids (prednisone, e.g.), central nervous system diseases or any disease process that causes polyphagia (increased hunger) such as diabetes mellitus, Cushing's disease, and hyperthyroidism might lead to picas (eating non-digestibles) and coprophagia. Calorie-restricted diets, especially those that are not balanced or do not adequately satiate the dog may also lead to picas including coprophagia. Recent research has suggested that there may indeed be a medical component to the problem in some cases. In a small study of nine coprophagic dogs, all had at least one laboratory abnormality that could explain the problem. The laboratory profile included a complete blood count, complete biochemical profile, amylase, lipase, trypsin-like immunoreactivity (TLI), vitamin B12, folate, fecal fat, fecal trypsin, fecal muscle fiber, trace minerals including zinc, selenium, copper, iron, magnesium and boron, and fecal sedimentation (an ova and parasite exam). Most had borderline to low TLI (suggesting pancreatic exocrine enzyme deficiency) while others had abnormalities in folate, Vitamin B12 (suggesting malabsorption) or other nutrients. As you can see, it might be wise to have blood work performed. Her vet can determine if all the above is necessary. For instance, checking trace mineral blood levels might be waived she is eating a high quality food.
Because I suspect a medical problem causing her coprophagia, it wouldn't be appropriate approaching her inappropiate elimination in the house until a medical disorder could be ruled out. Disorders that cause gastrointestinal discomfort might well predispose to inappropriate eliminative behavior. Please respond with further questions or concerns if you wish.