Nephrotic Syndrome: Given the patient's stable schizophrenia, the new onset of bilateral lower leg pitting edema, worsening anemia (with a significant hemoglobin drop), and low sodium levels, nephrotic syndrome is a strong consideration. The condition is characterized by heavy proteinuria, hypoalbuminemia, hyperlipidemia, and edema. The low sodium could be indicative of nephrotic syndrome due to the loss of albumin and subsequent decrease in oncotic pressure, leading to fluid shift into the interstitial space.

Deep Vein Thrombosis (DVT): The positive D-dimer and new onset of bilateral lower leg edema make DVT a likely diagnosis. Although DVT typically presents unilaterally, bilateral DVTs can occur, especially in the context of a hypercoagulable state or severe immobility.
Chronic Kidney Disease (CKD): CKD could explain the worsening anemia and low sodium levels. Anemia in CKD is due to decreased erythropoietin production, and sodium imbalances can occur due to the kidney's inability to properly regulate electrolytes.
Heart Failure: This condition could lead to bilateral lower extremity edema due to fluid overload and decreased cardiac output. The worsening anemia could also contribute to or exacerbate heart failure symptoms.

Pulmonary Embolism (PE): Although the presentation does not classically suggest PE, the positive D-dimer is a red flag. A significant and acute drop in hemoglobin could also be seen in the context of a large PE causing right heart strain and subsequent decrease in cardiac output.
Abdominal or Pelvic Mass: A mass compressing the inferior vena cava or iliac veins could cause bilateral lower extremity edema. This would be an unusual presentation but is crucial not to miss due to the potential for malignancy.
Disseminated Intravascular Coagulation (DIC): Given the significant drop in hemoglobin and positive D-dimer, DIC should be considered, especially if there are other signs of coagulopathy or a known precipitant.

Lymphoma or Other Malignancy: Certain malignancies can cause nephrotic syndrome or CKD, leading to edema and electrolyte imbalances. Lymphoma can also cause anemia and is a consideration in a patient with unexplained significant hemoglobin drop.
Amyloidosis: This condition can cause nephrotic syndrome, CKD, and heart failure, leading to edema and electrolyte disturbances. It is rare but should be considered in the differential diagnosis of unexplained nephrotic syndrome or CKD.
Thyroid Disorder: Both hypothyroidism and hyperthyroidism can cause edema, although this is typically not pitting. Significant anemia can also be seen in severe thyroid disorders.