Final answer:
The most likely concurrent injury to accompany a lumbar spine fracture when falling and landing on the feet is a fracture of the lower extremity, specifically a Pott's fracture of the ankle involving a fracture of the distal fibula.
Step-by-step explanation:
A patient who lands on their feet after jumping from a second-floor window is experiencing a high-impact force on the lower extremities and spine. The immediate and intense force upon landing can result in injuries that extend beyond a lumbar spine fracture. Given the context of a high-energy fall, the most likely concurrent injury is a fracture of the lower extremity, specifically, the distal fibula. This is due to the mechanism of forcible lateral movement of the talus, known as a Pott's fracture, which is an eversion injury that can lead to the medial malleolus of the tibia being sheared off, causing the talus to dislocate laterally and fracture the distal fibula.
Upon impact, the ankle, being the most frequently injured joint in the body, is at significant risk. An inversion ankle sprain resulting in damage to the anterior talofibular ligament followed by the calcaneofibular ligament may occur, but given the severity of the landing, it is more likely that the force would result in fractures rather than sprains.