**Core Concept:**
The question is testing the understanding of the site where lymphocytes, a type of white blood cell, acquire their immunocompetence - the ability to recognize and respond to foreign antigens. This process takes place in specialized lymphoid organs called lymphoid tissues.

**Why the Correct Answer is Right:**
Lymphocytes are produced in the bone marrow and then migrate to peripheral lymphoid organs where they mature and become immunocompetent. These organs include the thymus (for T-cells) and the bone marrow (for B-cells). In the thymus, T-cells undergo a process called positive and negative selection to ensure they can recognize and respond to foreign antigens without attacking self-cells. In the bone marrow, B-cells differentiate and mature into plasma cells that produce antibodies specific to foreign antigens.

**Why Each Wrong Option is Incorrect:**
A. Spleen: While the spleen does play a role in the immune response, lymphocytes do not become immunocompetent within it.
B. Peripheral lymph nodes: While lymphocytes do enter and recirculate through peripheral lymph nodes, they do not become immunocompetent here.
C. Thymus: Lymphocytes become immunocompetent in the thymus, not the spleen or peripheral lymph nodes.
D. Peripheral blood: Lymphocytes are found in the peripheral blood but do not become immunocompetent here.

**Clinical Pearl:**
Understanding the development and maturation of lymphocytes is essential for understanding immune responses and various immune-related diseases. Adequate knowledge of these sites is crucial for diagnosing and treating patients with immunodeficiencies or autoimmune disorders involving lymphocytes.

**Correct Answer:** C. Thymus

In conclusion, lymphocytes become immunocompetent in the thymus, ensuring that T-cells can recognize and respond to foreign antigens without attacking self-cells, thus maintaining immunological tolerance.