**Core Concept**
Ventrolateral cordotomy is a surgical procedure used to relieve chronic pain by interrupting the spinothalamic tract, a critical pathway for pain transmission in the spinal cord. This procedure targets the lateral spinothalamic tract, which carries pain and temperature sensations from the body to the brain.

**Why the Correct Answer is Right**
The ventrolateral cordotomy effectively relieves pain in the left lower limb by cutting the lateral spinothalamic tract, which is responsible for transmitting pain and temperature sensations from the left lower limb to the brain. The lateral spinothalamic tract is composed of axons that originate from the spinal cord and ascend through the lateral funiculus of the spinal cord to the thalamus, where the pain and temperature information is processed. By cutting this tract, the transmission of pain signals from the left lower limb to the brain is interrupted, providing pain relief.

**Why Each Wrong Option is Incorrect**
* **Option A:** The posterior column-medial lemniscus pathway is responsible for transmitting proprioception, vibration, and fine touch sensations from the body to the brain. Cutting this pathway would not relieve pain in the left lower limb.
* **Option B:** The anterior spinothalamic tract is responsible for transmitting crude touch and pressure sensations from the body to the brain. While it is involved in the transmission of sensory information, it is not the primary target for pain relief in ventrolateral cordotomy.
* **Option D:** The corticospinal tract is responsible for motor function and is not involved in the transmission of pain or sensory information.

**Clinical Pearl / High-Yield Fact**
To remember the target of ventrolateral cordotomy, recall that the "lateral" spinothalamic tract is involved in the transmission of pain and temperature sensations, and that the procedure aims to interrupt this tract to provide pain relief.

**Correct Answer:** C. The lateral spinothalamic tract