S1 Radiculopathy: This is the most likely diagnosis due to the common involvement of the S1 nerve root in lumbar disc herniations, which can cause pain radiating down to the lateral calf.

Lumbar Disc Herniation: A herniated disc in the lumbar spine can compress or irritate nearby nerves, leading to pain that radiates to the lateral calf.
Lumbar Spondylosis: Degenerative changes in the lumbar spine can cause nerve root compression or irritation, resulting in radiating pain.
Piriformis Syndrome: The piriformis muscle can compress the sciatic nerve, causing pain that radiates down the leg, including the lateral calf.

Cauda Equina Syndrome: A serious condition where the nerves in the spinal canal are compressed, which can lead to severe neurological deficits if not promptly treated.
Spinal Infection (e.g., Abscess or Osteomyelitis): Infections in the spine can cause severe back pain and radiating pain, and require urgent medical attention.
Spinal Tumor: Tumors in the spine can compress nerves, leading to radiating pain, and are critical to diagnose early.

Peripheral Artery Disease: Although more common in the elderly, PAD can cause leg pain that may be mistaken for radiating back pain.
Nerve Sheath Tumor: Benign tumors that arise from the nerve sheath can compress adjacent nerves, leading to radiating pain.
Tarlov Cyst: A rare condition where a cyst forms on the nerve root, which can cause pain and neurological symptoms.