Final answer:
A lymphocyte with cytoplasmic azurophilic granules is most likely a granulocyte, such as a neutrophil, eosinophil, or basophil.
Step-by-step explanation:
A lymphocyte with cytoplasmic azurophilic granules on the peripheral smear is most likely a granulocyte. Granulocytes are a type of leukocytes characterized by numerous granules in the cytoplasm. The three types of granulocytes are neutrophils, eosinophils, and basophils. Neutrophils have small granules that stain light lilac, eosinophils have slightly larger granules that stain reddish-orange, and basophils have large granules that stain dark blue to purple.