**Core Concept**
The brachial cyst, also known as a brachial cleft cyst, is a type of congenital anomaly that arises from the **embryological remnants** of the second branchial cleft. It is essential to understand the **histological composition** of such cysts to determine their lining.

**Why the Correct Answer is Right**
The correct answer is related to the **squamous epithelium**, which is the typical lining of brachial cleft cysts. This lining is a result of the cyst's origin from the **branchial apparatus**, specifically the second branchial cleft, which is lined by **squamous epithelial cells**.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it does not accurately describe the lining of a brachial cyst.
**Option B:** Similarly, this option is incorrect as it is not the typical lining of such cysts.
**Option D:** This option is also incorrect as the lining of a brachial cyst is not composed of this type of tissue.

**Clinical Pearl / High-Yield Fact**
It is crucial to remember that brachial cleft cysts are usually lined by **squamous epithelium**, which is a key feature in their diagnosis. This knowledge can help in distinguishing them from other types of cysts.

**Correct Answer:** C. Squamous epithelium