**Core Concept**
The femoral sheath is a tubular extension of the fascia transversalis that encloses the femoral vessels and nerves. It is a key anatomical structure in the region of the femoral canal, and its relationship to surrounding structures is crucial for surgical and clinical considerations.

**Why the Correct Answer is Right**
The femoral sheath is a condensation of the fascia transversalis that surrounds the femoral vessels and nerves. The femoral vein lies lateral to the femoral sheath, meaning it is positioned on the outside of the sheath. This is in contrast to the femoral artery, which lies within the medial wall of the sheath. The lateral cutaneous nerve of the thigh and femoral nerve are also found outside the femoral sheath, but the correct answer is the femoral vein due to its specific relationship with the sheath.

**Why Each Wrong Option is Incorrect**
**Option A:** The femoral artery lies within the medial wall of the femoral sheath, not lateral to it.
**Option B:** While the lateral cutaneous nerve of the thigh does lie outside the femoral sheath, it is not the correct answer because the question specifically asks for a structure that lies lateral to the sheath.
**Option D:** The femoral nerve lies outside the femoral sheath, but it is not the correct answer because the question is asking for a structure that is specifically lateral to the sheath.

**Clinical Pearl / High-Yield Fact**
In the context of femoral hernias, it is essential to recognize the relationship between the sheath and the surrounding structures. The femoral vein's position lateral to the sheath is critical for surgeons to avoid damaging during hernia repair.

**✓ Correct Answer: C. Femoral vein**