Lymphoma: This is a type of cancer that affects the immune system and can cause enlargement of the liver (hepatomegaly), spleen (splenomegaly), and lymph nodes, leading to lymphedema. The combination of these symptoms strongly suggests a lymphatic system malignancy.

Chronic Liver Disease: Conditions like cirrhosis can lead to hepatomegaly and splenomegaly due to portal hypertension. Lymphedema might be less directly related but could occur due to hypoalbuminemia or other secondary effects.
Portal Hypertension: Often a result of chronic liver disease, portal hypertension can cause splenomegaly and hepatomegaly. Lymphedema could be a consequence of the increased pressure and fluid accumulation.
Infectious Diseases (e.g., Tuberculosis, Endemic Mycoses): Certain infections can cause hepatosplenomegaly and, in some cases, lymphedema, especially if there's significant lymph node involvement.

Lymphangiosarcoma: A rare and aggressive cancer that arises from the lymphatic vessels, often presenting with lymphedema. It's crucial to consider this diagnosis due to its poor prognosis and the need for early intervention.
Kaposi's Sarcoma: This cancer can involve the lymphatic system and present with lymphedema, hepatomegaly, and splenomegaly, especially in immunocompromised patients.
Systemic Lupus Erythematosus (SLE): An autoimmune disease that can affect multiple systems, including the liver, spleen, and lymphatic system, potentially causing the symptoms in question.

Gaucher's Disease: A genetic disorder that can lead to hepatosplenomegaly due to the accumulation of glucocerebroside. Lymphedema is less common but can occur.
Niemann-Pick Disease: Another genetic disorder that affects lipid metabolism, leading to hepatosplenomegaly and potentially lymphedema due to systemic involvement.
Lymphatic Malformations: Congenital conditions that affect the development of the lymphatic system, which can cause lymphedema and, in some cases, hepatosplenomegaly if there's significant systemic involvement.