**Core Concept**
Intraductal carcinoma, also known as ductal carcinoma in situ (DCIS), is a type of non-invasive breast cancer where the cancer cells are confined to the milk ducts of the breast. The initial management of a patient with a breast lump showing intraductal carcinoma involves a multidisciplinary approach, including surgical, radiological, and pathological evaluation.

**Why the Correct Answer is Right**
The correct initial management for a patient with a breast lump showing intraductal carcinoma involves a diagnostic biopsy to confirm the extent of the disease. A core needle biopsy is often performed to obtain tissue for histopathological examination and to determine the presence of cancer cells in the milk ducts. In this case, the patient already underwent FNAC, which showed intraductal carcinoma. A definitive diagnosis can be made with a core needle biopsy or a surgical biopsy. The management plan will also include imaging studies, such as mammography and ultrasound, to evaluate the extent of the disease and assess for any regional lymph node involvement.

**Why Each Wrong Option is Incorrect**
* **Option A:** is incorrect because mastectomy is not the initial management for intraductal carcinoma, as it is a non-invasive form of breast cancer.
* **Option B:** is incorrect because lumpectomy is not the initial management for intraductal carcinoma, as it is a non-invasive form of breast cancer and the extent of the disease is not well-defined.
* **Option D:** is incorrect because sentinel lymph node biopsy is not the initial management for intraductal carcinoma, as it is a non-invasive form of breast cancer and the extent of the disease is not well-defined.

**Clinical Pearl / High-Yield Fact**
In patients with intraductal carcinoma, a core needle biopsy is essential to confirm the diagnosis and to determine the extent of the disease. A definitive diagnosis can only be made with a core needle biopsy or a surgical biopsy.

**Correct Answer:** C.