Chronic Myeloid Leukemia (CML): This condition is characterized by an overproduction of granulocytes, but it can also present with lymphocytosis. Priapism is a known, though rare, complication of CML, likely due to increased blood viscosity or leukostasis.

Chronic Lymphocytic Leukemia (CLL): CLL is a type of cancer that affects the blood and bone marrow, characterized by the production of an excessive number of immature white blood cells. While priapism is not a common presentation, the lymphocytosis associated with CLL could potentially lead to increased blood viscosity, which might contribute to priapism.
Polycythemia Vera: This is a myeloproliferative disorder that can lead to an overproduction of all three blood cell types. It can cause increased blood viscosity, which may lead to priapism. Lymphocytosis can be seen in some cases, although it's not the primary feature.

Sickle Cell Disease: Although more commonly associated with anemia, sickle cell disease can cause priapism due to sickling of red blood cells leading to vaso-occlusion. Lymphocytosis might not be a primary feature, but it's crucial to consider this diagnosis due to its potential severity and the fact that patients with sickle cell disease can have varying blood cell counts.
Leukemia (other types): Other leukemias, such as acute lymphoblastic leukemia (ALL) or acute myeloid leukemia (AML), can present with lymphocytosis and, in rare cases, priapism due to leukostasis or tumor lysis syndrome.

Lymphoma: Certain types of lymphoma can cause lymphocytosis. While priapism is extremely rare in lymphoma, it could potentially occur due to compression or infiltration of pelvic structures by lymphomatous tissue.
Myeloproliferative Neoplasms (other): Besides CML and Polycythemia Vera, other myeloproliferative neoplasms like Essential Thrombocythemia or Primary Myelofibrosis could theoretically lead to lymphocytosis and priapism, though this would be uncommon.