Final answer:
T lymphocytes develop immunocompetence in the thymus.
Step-by-step explanation:
The lymphocytes that develop immunocompetence in the thymus are T lymphocytes. T cells migrate from the bone marrow to the thymus gland where they further mature and develop their T cell receptors. The thymus plays a crucial role in the maturation and selection of T cells, allowing them to recognize and respond to specific antigens.